Brzina – Wikipedija/Википедија

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title=\"Wikipedija:Mjesec Azije/2024\"\u003EMjesec Azije\u003C/a\u003E. \u003C/td\u003E\n\u003C/tr\u003E\n\u003C/tbody\u003E\u003C/table\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sajt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Sadržaj" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Sadržaj</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">premjesti na bočnu traku</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sakrij</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Početak</div> </a> </li> <li id="toc-Terminologija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Terminologija"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Terminologija</span> </div> </a> <ul id="toc-Terminologija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Konstantna_brzina" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Konstantna_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Konstantna brzina</span> </div> </a> <button aria-controls="toc-Konstantna_brzina-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uključi/isključi podsekciju Konstantna brzina</span> </button> <ul id="toc-Konstantna_brzina-sublist" class="vector-toc-list"> <li id="toc-Konstantna_brzina_ili_ubrzanje" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Konstantna_brzina_ili_ubrzanje"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Konstantna brzina ili ubrzanje</span> </div> </a> <ul id="toc-Konstantna_brzina_ili_ubrzanje-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Trenutna_brzina_i_trenutna_putna_brzina" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Trenutna_brzina_i_trenutna_putna_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Trenutna brzina i trenutna putna brzina</span> </div> </a> <button aria-controls="toc-Trenutna_brzina_i_trenutna_putna_brzina-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uključi/isključi podsekciju Trenutna brzina i trenutna putna brzina</span> </button> <ul id="toc-Trenutna_brzina_i_trenutna_putna_brzina-sublist" class="vector-toc-list"> <li id="toc-Trenutna_brzina" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Trenutna_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Trenutna brzina</span> </div> </a> <ul id="toc-Trenutna_brzina-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Trenutna_putna_brzina" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Trenutna_putna_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Trenutna putna brzina</span> </div> </a> <ul id="toc-Trenutna_putna_brzina-sublist" class="vector-toc-list"> <li id="toc-Razlika_između_trenutne_brzine_i_trenutne_putne_brzine" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Razlika_između_trenutne_brzine_i_trenutne_putne_brzine"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>Razlika između trenutne brzine i trenutne putne brzine</span> </div> </a> <ul id="toc-Razlika_između_trenutne_brzine_i_trenutne_putne_brzine-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Srednja_brzina_i_srednja_putna_brzina" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Srednja_brzina_i_srednja_putna_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Srednja brzina i srednja putna brzina</span> </div> </a> <button aria-controls="toc-Srednja_brzina_i_srednja_putna_brzina-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uključi/isključi podsekciju Srednja brzina i srednja putna brzina</span> </button> <ul id="toc-Srednja_brzina_i_srednja_putna_brzina-sublist" class="vector-toc-list"> <li id="toc-Srednja_brzina" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Srednja_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Srednja brzina</span> </div> </a> <ul id="toc-Srednja_brzina-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Srednja_putna_brzina" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Srednja_putna_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Srednja putna brzina</span> </div> </a> <ul id="toc-Srednja_putna_brzina-sublist" class="vector-toc-list"> <li id="toc-Razlika_između_srednje_brzine_i_srednje_putne_brzine" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Razlika_između_srednje_brzine_i_srednje_putne_brzine"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>Razlika između srednje brzine i srednje putne brzine</span> </div> </a> <ul id="toc-Razlika_između_srednje_brzine_i_srednje_putne_brzine-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Jednačine_kretanja" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Jednačine_kretanja"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Jednačine kretanja</span> </div> </a> <button aria-controls="toc-Jednačine_kretanja-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uključi/isključi podsekciju Jednačine kretanja</span> </button> <ul id="toc-Jednačine_kretanja-sublist" class="vector-toc-list"> <li id="toc-Konstantno_ubrzanje" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Konstantno_ubrzanje"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Konstantno ubrzanje</span> </div> </a> <ul id="toc-Konstantno_ubrzanje-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Veličine_zavisne_o_brzini" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Veličine_zavisne_o_brzini"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Veličine zavisne o brzini</span> </div> </a> <ul id="toc-Veličine_zavisne_o_brzini-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relativna_brzina" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relativna_brzina"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Relativna brzina</span> </div> </a> <button aria-controls="toc-Relativna_brzina-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uključi/isključi podsekciju Relativna brzina</span> </button> <ul id="toc-Relativna_brzina-sublist" class="vector-toc-list"> <li id="toc-Skalari" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Skalari"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Skalari</span> </div> </a> <ul id="toc-Skalari-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Polarne_koordinate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Polarne_koordinate"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Polarne koordinate</span> </div> </a> <ul id="toc-Polarne_koordinate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Povezano" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Povezano"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Povezano</span> </div> </a> <ul id="toc-Povezano-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Literatura" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Literatura"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Literatura</span> </div> </a> <ul id="toc-Literatura-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vanjske_veze" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vanjske_veze"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>Vanjske veze</span> </div> </a> <ul id="toc-Vanjske_veze-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" lang="sh-Latn" dir="ltr"> <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Prikaži/sakrij sadržaj" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Prikaži/sakrij sadržaj</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading" lang="sh-Latn" dir="ltr"><span class="mw-page-title-main">Brzina</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" lang="sh-Latn" dir="ltr"> <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Prijedi na druge jezične varijante članka. Dostupno je na 130 jezika" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-130" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">130 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Snelheid" title="Snelheid — Afrikanerski" lang="af" hreflang="af" data-title="Snelheid" data-language-autonym="Afrikaans" data-language-local-name="Afrikanerski" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Geschwindigkeit" title="Geschwindigkeit — Švajcarsko nemački" lang="gsw" hreflang="gsw" data-title="Geschwindigkeit" data-language-autonym="Alemannisch" data-language-local-name="Švajcarsko nemački" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8D%8D%E1%8C%A5%E1%8A%90%E1%89%B5" title="ፍጥነት — Amharski" lang="am" hreflang="am" data-title="ፍጥነት" data-language-autonym="አማርኛ" data-language-local-name="Amharski" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Velocidat" title="Velocidat — Aragonežanski" lang="an" hreflang="an" data-title="Velocidat" data-language-autonym="Aragonés" data-language-local-name="Aragonežanski" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%B5%E0%A5%87%E0%A4%97" title="वेग — Angika" lang="anp" hreflang="anp" data-title="वेग" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B3%D8%B1%D8%B9%D8%A9_%D9%85%D8%AA%D8%AC%D9%87%D8%A9" title="سرعة متجهة — Arapski" lang="ar" hreflang="ar" data-title="سرعة متجهة" data-language-autonym="العربية" data-language-local-name="Arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A7%87%E0%A6%97" title="বেগ — Asemijski" lang="as" hreflang="as" data-title="বেগ" data-language-autonym="অসমীয়া" data-language-local-name="Asemijski" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Velocid%C3%A1" title="Velocidá — Asturijski" lang="ast" hreflang="ast" data-title="Velocidá" data-language-autonym="Asturianu" data-language-local-name="Asturijski" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DB%8C%D8%A4%D9%86%D8%A6%DB%8C%D9%84%DB%8C_%D8%B3%D9%88%D8%B1%D8%B9%D8%AA" title="یؤنئیلی سورعت — South Azerbaijani" lang="azb" hreflang="azb" data-title="یؤنئیلی سورعت" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A2%D0%B8%D2%99%D0%BB%D0%B5%D0%BA" title="Тиҙлек — Baškir" lang="ba" hreflang="ba" data-title="Тиҙлек" data-language-autonym="Башҡортса" data-language-local-name="Baškir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Gschwindigkeit" title="Gschwindigkeit — Bavarian" lang="bar" hreflang="bar" data-title="Gschwindigkeit" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Belosidad" title="Belosidad — Central Bikol" lang="bcl" hreflang="bcl" data-title="Belosidad" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D0%BA%D0%BE%D1%80%D0%B0%D1%81%D1%86%D1%8C" title="Скорасць — Beloruski" lang="be" hreflang="be" data-title="Скорасць" data-language-autonym="Беларуская" data-language-local-name="Beloruski" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A5%D1%83%D1%82%D0%BA%D0%B0%D1%81%D1%8C%D1%86%D1%8C" title="Хуткасьць — Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Хуткасьць" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82" title="Скорост — Bugarski" lang="bg" hreflang="bg" data-title="Скорост" data-language-autonym="Български" data-language-local-name="Bugarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%B5%E0%A5%87%E0%A4%97" title="वेग — Biharski" lang="bh" hreflang="bh" data-title="वेग" data-language-autonym="भोजपुरी" data-language-local-name="Biharski" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A7%87%E0%A6%97" title="গতিবেগ — Bengalski" lang="bn" hreflang="bn" data-title="গতিবেগ" data-language-autonym="বাংলা" data-language-local-name="Bengalski" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Brzina" title="Brzina — Bosanski" lang="bs" hreflang="bs" data-title="Brzina" data-language-autonym="Bosanski" data-language-local-name="Bosanski" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%A5%D1%83%D1%80%D0%B4%D0%B0%D0%BD" title="Хурдан — Russia Buriat" lang="bxr" hreflang="bxr" data-title="Хурдан" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Velocitat" title="Velocitat — Katalonski" lang="ca" hreflang="ca" data-title="Velocitat" data-language-autonym="Català" data-language-local-name="Katalonski" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/S%C3%B3k-d%C3%B4" title="Sók-dô — Mindong" lang="cdo" hreflang="cdo" data-title="Sók-dô" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%A1%D0%B8%D1%85%D0%B0%D0%BB%D0%BB%D0%B0" title="Сихалла — Čečenski" lang="ce" hreflang="ce" data-title="Сихалла" data-language-autonym="Нохчийн" data-language-local-name="Čečenski" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Tulin_(pisika)" title="Tulin (pisika) — Cebuano" lang="ceb" hreflang="ceb" data-title="Tulin (pisika)" data-language-autonym="Cebuano" data-language-local-name="Cebuano" class="interlanguage-link-target"><span>Cebuano</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AE%DB%8E%D8%B1%D8%A7%DB%8C%DB%8C_(%D9%81%DB%8C%D8%B2%DB%8C%DA%A9)" title="خێرایی (فیزیک) — centralnokurdski" lang="ckb" hreflang="ckb" data-title="خێرایی (فیزیک)" data-language-autonym="کوردی" data-language-local-name="centralnokurdski" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Rychlost" title="Rychlost — Češki" lang="cs" hreflang="cs" data-title="Rychlost" data-language-autonym="Čeština" data-language-local-name="Češki" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A5%C4%83%D0%B2%C4%83%D1%80%D1%82%D0%BB%C4%83%D1%85" title="Хăвăртлăх — Čuvaški" lang="cv" hreflang="cv" data-title="Хăвăртлăх" data-language-autonym="Чӑвашла" data-language-local-name="Čuvaški" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Cyflymder" title="Cyflymder — Velški" lang="cy" hreflang="cy" data-title="Cyflymder" data-language-autonym="Cymraeg" data-language-local-name="Velški" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hastighed" title="Hastighed — Danski" lang="da" hreflang="da" data-title="Hastighed" data-language-autonym="Dansk" data-language-local-name="Danski" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Geschwindigkeit" title="Geschwindigkeit — Nemački" lang="de" hreflang="de" data-title="Geschwindigkeit" data-language-autonym="Deutsch" data-language-local-name="Nemački" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CE%B1%CF%87%CF%8D%CF%84%CE%B7%CF%84%CE%B1" title="Ταχύτητα — Grčki" lang="el" hreflang="el" data-title="Ταχύτητα" data-language-autonym="Ελληνικά" data-language-local-name="Grčki" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Velocity" title="Velocity — Engleski" lang="en" hreflang="en" data-title="Velocity" data-language-autonym="English" data-language-local-name="Engleski" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Vektora_rapido" title="Vektora rapido — Esperanto" lang="eo" hreflang="eo" data-title="Vektora rapido" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Velocidad" title="Velocidad — Španski" lang="es" hreflang="es" data-title="Velocidad" data-language-autonym="Español" data-language-local-name="Španski" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kiirus" title="Kiirus — Estonski" lang="et" hreflang="et" data-title="Kiirus" data-language-autonym="Eesti" data-language-local-name="Estonski" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Abiadura" title="Abiadura — Baskijski" lang="eu" hreflang="eu" data-title="Abiadura" data-language-autonym="Euskara" data-language-local-name="Baskijski" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Velocid%C3%A1" title="Velocidá — Extremaduran" lang="ext" hreflang="ext" data-title="Velocidá" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B3%D8%B1%D8%B9%D8%AA_%D8%A8%D8%B1%D8%AF%D8%A7%D8%B1%DB%8C" title="سرعت برداری — Persijski" lang="fa" hreflang="fa" data-title="سرعت برداری" data-language-autonym="فارسی" data-language-local-name="Persijski" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Nopeus" title="Nopeus — Finski" lang="fi" hreflang="fi" data-title="Nopeus" data-language-autonym="Suomi" data-language-local-name="Finski" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Kib%C3%B5husvektor" title="Kibõhusvektor — Võro" lang="vro" hreflang="vro" data-title="Kibõhusvektor" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Vecteur_vitesse" title="Vecteur vitesse — Francuski" lang="fr" hreflang="fr" data-title="Vecteur vitesse" data-language-autonym="Français" data-language-local-name="Francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Faard" title="Faard — Severno-frizijski" lang="frr" hreflang="frr" data-title="Faard" data-language-autonym="Nordfriisk" data-language-local-name="Severno-frizijski" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Faasje" title="Faasje — Frizijski" lang="fy" hreflang="fy" data-title="Faasje" data-language-autonym="Frysk" data-language-local-name="Frizijski" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Treoluas" title="Treoluas — Irski" lang="ga" hreflang="ga" data-title="Treoluas" data-language-autonym="Gaeilge" data-language-local-name="Irski" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Velocidade" title="Velocidade — Galski" lang="gl" hreflang="gl" data-title="Velocidade" data-language-autonym="Galego" data-language-local-name="Galski" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Bieauid-jeerit" title="Bieauid-jeerit — Manks" lang="gv" hreflang="gv" data-title="Bieauid-jeerit" data-language-autonym="Gaelg" data-language-local-name="Manks" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%94%D7%99%D7%A8%D7%95%D7%AA" title="מהירות — Hebrejski" lang="he" hreflang="he" data-title="מהירות" data-language-autonym="עברית" data-language-local-name="Hebrejski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A5%87%E0%A4%97" title="वेग — Hindi" lang="hi" hreflang="hi" data-title="वेग" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Raftaar" title="Raftaar — Fiji Hindi" lang="hif" hreflang="hif" data-title="Raftaar" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Brzina" title="Brzina — Hrvatski" lang="hr" hreflang="hr" data-title="Brzina" data-language-autonym="Hrvatski" data-language-local-name="Hrvatski" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Velosite" title="Velosite — Haićanski" lang="ht" hreflang="ht" data-title="Velosite" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haićanski" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Sebess%C3%A9g" title="Sebesség — Mađarski" lang="hu" hreflang="hu" data-title="Sebesség" data-language-autonym="Magyar" data-language-local-name="Mađarski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D6%80%D5%A1%D5%A3%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Արագություն — Jermenski" lang="hy" hreflang="hy" data-title="Արագություն" data-language-autonym="Հայերեն" data-language-local-name="Jermenski" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Velocitate" title="Velocitate — Interlingva" lang="ia" hreflang="ia" data-title="Velocitate" data-language-autonym="Interlingua" data-language-local-name="Interlingva" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kecepatan" title="Kecepatan — Indonezijski" lang="id" hreflang="id" data-title="Kecepatan" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonezijski" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ie mw-list-item"><a href="https://ie.wikipedia.org/wiki/Velocit%C3%A1" title="Velocitá — Interlingve" lang="ie" hreflang="ie" data-title="Velocitá" data-language-autonym="Interlingue" data-language-local-name="Interlingve" class="interlanguage-link-target"><span>Interlingue</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Hra%C3%B0i" title="Hraði — Islandski" lang="is" hreflang="is" data-title="Hraði" data-language-autonym="Íslenska" data-language-local-name="Islandski" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Velocit%C3%A0" title="Velocità — Italijanski" lang="it" hreflang="it" data-title="Velocità" data-language-autonym="Italiano" data-language-local-name="Italijanski" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%80%9F%E5%BA%A6" title="速度 — Japanski" lang="ja" hreflang="ja" data-title="速度" data-language-autonym="日本語" data-language-local-name="Japanski" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Kacepetan" title="Kacepetan — Javanski" lang="jv" hreflang="jv" data-title="Kacepetan" data-language-autonym="Jawa" data-language-local-name="Javanski" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%98%E1%83%A9%E1%83%A5%E1%83%90%E1%83%A0%E1%83%94" title="სიჩქარე — Gruzijski" lang="ka" hreflang="ka" data-title="სიჩქარე" data-language-autonym="ქართული" data-language-local-name="Gruzijski" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Arured_amaway" title="Arured amaway — Kabile" lang="kab" hreflang="kab" data-title="Arured amaway" data-language-autonym="Taqbaylit" data-language-local-name="Kabile" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%96%D1%8B%D0%BB%D0%B4%D0%B0%D0%BC%D0%B4%D1%8B%D2%9B" title="Жылдамдық — Kozački" lang="kk" hreflang="kk" data-title="Жылдамдық" data-language-autonym="Қазақша" data-language-local-name="Kozački" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%9B%E1%9F%92%E1%9E%94%E1%9E%BF%E1%9E%93" title="ល្បឿន — Kmerski" lang="km" hreflang="km" data-title="ល្បឿន" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Kmerski" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B5%E0%B3%87%E0%B2%97" title="ವೇಗ — Kanada" lang="kn" hreflang="kn" data-title="ವೇಗ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kanada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%86%8D%EB%8F%84" title="속도 — Korejski" lang="ko" hreflang="ko" data-title="속도" data-language-autonym="한국어" data-language-local-name="Korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%D9%88%DB%8C%D9%96%DA%AF" title="ویٖگ — Kašmiri" lang="ks" hreflang="ks" data-title="ویٖگ" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="Kašmiri" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Uskitter" title="Uskitter — Korniški" lang="kw" hreflang="kw" data-title="Uskitter" data-language-autonym="Kernowek" data-language-local-name="Korniški" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Velocitas" title="Velocitas — Latinski" lang="la" hreflang="la" data-title="Velocitas" data-language-autonym="Latina" data-language-local-name="Latinski" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Rapidia_vetoral" title="Rapidia vetoral — Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Rapidia vetoral" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Snelheid" title="Snelheid — Limburgiš" lang="li" hreflang="li" data-title="Snelheid" data-language-autonym="Limburgs" data-language-local-name="Limburgiš" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Velocitaa" title="Velocitaa — lombardski" lang="lmo" hreflang="lmo" data-title="Velocitaa" data-language-autonym="Lombard" data-language-local-name="lombardski" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Vektorinis_greitis" title="Vektorinis greitis — Litvanski" lang="lt" hreflang="lt" data-title="Vektorinis greitis" data-language-autonym="Lietuvių" data-language-local-name="Litvanski" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C4%80trums" title="Ātrums — Letonski" lang="lv" hreflang="lv" data-title="Ātrums" data-language-autonym="Latviešu" data-language-local-name="Letonski" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Hafainganam-pandeha" title="Hafainganam-pandeha — Malagazijski" lang="mg" hreflang="mg" data-title="Hafainganam-pandeha" data-language-autonym="Malagasy" data-language-local-name="Malagazijski" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Laju" title="Laju — Minangkabau" lang="min" hreflang="min" data-title="Laju" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D1%80%D0%B7%D0%B8%D0%BD%D0%B0" title="Брзина — Makedonski" lang="mk" hreflang="mk" data-title="Брзина" data-language-autonym="Македонски" data-language-local-name="Makedonski" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%B5%E0%B5%87%E0%B4%97%E0%B4%82" title="പ്രവേഗം — Malajalam" lang="ml" hreflang="ml" data-title="പ്രവേഗം" data-language-autonym="മലയാളം" data-language-local-name="Malajalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D1%83%D1%80%D0%B4" title="Хурд — Mongolski" lang="mn" hreflang="mn" data-title="Хурд" data-language-autonym="Монгол" data-language-local-name="Mongolski" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B5%E0%A5%87%E0%A4%97" title="वेग — Marati" lang="mr" hreflang="mr" data-title="वेग" data-language-autonym="मराठी" data-language-local-name="Marati" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Halaju" title="Halaju — Malajski" lang="ms" hreflang="ms" data-title="Halaju" data-language-autonym="Bahasa Melayu" data-language-local-name="Malajski" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%9C%E1%80%BB%E1%80%84%E1%80%BA" title="အလျင် — Burmanski" lang="my" hreflang="my" data-title="အလျင်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmanski" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%9C%D0%BE%D0%BB%D0%B5%D0%B2%D0%BA%D1%81" title="Молевкс — Erzija" lang="myv" hreflang="myv" data-title="Молевкс" data-language-autonym="Эрзянь" data-language-local-name="Erzija" class="interlanguage-link-target"><span>Эрзянь</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Snelligkeid" title="Snelligkeid — Niski nemački" lang="nds" hreflang="nds" data-title="Snelligkeid" data-language-autonym="Plattdüütsch" data-language-local-name="Niski nemački" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%97%E0%A4%A4%E0%A4%BF" title="गति — Nepalski" lang="ne" hreflang="ne" data-title="गति" data-language-autonym="नेपाली" data-language-local-name="Nepalski" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Snelheid" title="Snelheid — Holandski" lang="nl" hreflang="nl" data-title="Snelheid" data-language-autonym="Nederlands" data-language-local-name="Holandski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Hastigheit" title="Hastigheit — Norveški njorsk" lang="nn" hreflang="nn" data-title="Hastigheit" data-language-autonym="Norsk nynorsk" data-language-local-name="Norveški njorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Hastighet" title="Hastighet — Norveški bokmål" lang="nb" hreflang="nb" data-title="Hastighet" data-language-autonym="Norsk bokmål" data-language-local-name="Norveški bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Velocitat" title="Velocitat — Provansalski" lang="oc" hreflang="oc" data-title="Velocitat" data-language-autonym="Occitan" data-language-local-name="Provansalski" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Ariitii" title="Ariitii — Oromo" lang="om" hreflang="om" data-title="Ariitii" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B5%E0%A9%87%E0%A8%97" title="ਵੇਗ — Pandžabski" lang="pa" hreflang="pa" data-title="ਵੇਗ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Pandžabski" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Pr%C4%99dko%C5%9B%C4%87" title="Prędkość — Poljski" lang="pl" hreflang="pl" data-title="Prędkość" data-language-autonym="Polski" data-language-local-name="Poljski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Andi" title="Andi — Piedmontese" lang="pms" hreflang="pms" data-title="Andi" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%88%D9%84%D8%A7%D8%B3%D9%B9%DB%8C" title="ولاسٹی — Western Punjabi" lang="pnb" hreflang="pnb" data-title="ولاسٹی" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Velocidade" title="Velocidade — Portugalski" lang="pt" hreflang="pt" data-title="Velocidade" data-language-autonym="Português" data-language-local-name="Portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Utqa_kay" title="Utqa kay — Kvenča" lang="qu" hreflang="qu" data-title="Utqa kay" data-language-autonym="Runa Simi" data-language-local-name="Kvenča" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Vitez%C4%83" title="Viteză — Rumunski" lang="ro" hreflang="ro" data-title="Viteză" data-language-autonym="Română" data-language-local-name="Rumunski" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82%D1%8C" title="Скорость — Ruski" lang="ru" hreflang="ru" data-title="Скорость" data-language-autonym="Русский" data-language-local-name="Ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A8%D0%B2%D1%8B%D0%B4%D0%BA%D0%BE%D1%81%D1%82%D1%8C" title="Швыдкость — Rusyn" lang="rue" hreflang="rue" data-title="Швыдкость" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sc badge-Q17437796 badge-featuredarticle mw-list-item" title="izabrani članci"><a href="https://sc.wikipedia.org/wiki/Velotzidade" title="Velotzidade — Sardinijski" lang="sc" hreflang="sc" data-title="Velotzidade" data-language-autonym="Sardu" data-language-local-name="Sardinijski" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D9%88%D9%8A%D9%84%D8%A7%D8%B3%D9%BD%D9%8A" title="ويلاسٽي — Sindi" lang="sd" hreflang="sd" data-title="ويلاسٽي" data-language-autonym="سنڌي" data-language-local-name="Sindi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%80%E0%B7%9A%E0%B6%9C%E0%B6%BA" title="ප්‍රවේගය — Singaleski" lang="si" hreflang="si" data-title="ප්‍රවේගය" data-language-autonym="සිංහල" data-language-local-name="Singaleski" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Velocity" title="Velocity — Simple English" lang="en-simple" hreflang="en-simple" data-title="Velocity" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/R%C3%BDchlos%C5%A5_(fyzik%C3%A1lna_veli%C4%8Dina)" title="Rýchlosť (fyzikálna veličina) — Slovački" lang="sk" hreflang="sk" data-title="Rýchlosť (fyzikálna veličina)" data-language-autonym="Slovenčina" data-language-local-name="Slovački" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Hitrost" title="Hitrost — Slovenački" lang="sl" hreflang="sl" data-title="Hitrost" data-language-autonym="Slovenščina" data-language-local-name="Slovenački" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-smn mw-list-item"><a href="https://smn.wikipedia.org/wiki/Li%C3%A4htu" title="Liähtu — Inari sami" lang="smn" hreflang="smn" data-title="Liähtu" data-language-autonym="Anarâškielâ" data-language-local-name="Inari sami" class="interlanguage-link-target"><span>Anarâškielâ</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Muchacha" title="Muchacha — Šona" lang="sn" hreflang="sn" data-title="Muchacha" data-language-autonym="ChiShona" data-language-local-name="Šona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Shpejt%C3%ABsia_(fizik%C3%AB)" title="Shpejtësia (fizikë) — Albanski" lang="sq" hreflang="sq" data-title="Shpejtësia (fizikë)" data-language-autonym="Shqip" data-language-local-name="Albanski" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D1%80%D0%B7%D0%B8%D0%BD%D0%B0" title="Брзина — Srpski" lang="sr" hreflang="sr" data-title="Брзина" data-language-autonym="Српски / srpski" data-language-local-name="Srpski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Hastighet" title="Hastighet — Švedski" lang="sv" hreflang="sv" data-title="Hastighet" data-language-autonym="Svenska" data-language-local-name="Švedski" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Kasimwelekeo" title="Kasimwelekeo — Svahili" lang="sw" hreflang="sw" data-title="Kasimwelekeo" data-language-autonym="Kiswahili" data-language-local-name="Svahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AE%BF%E0%AE%9A%E0%AF%88%E0%AE%B5%E0%AF%87%E0%AE%95%E0%AE%AE%E0%AF%8D" title="திசைவேகம் — Tamilski" lang="ta" hreflang="ta" data-title="திசைவேகம்" data-language-autonym="தமிழ்" data-language-local-name="Tamilski" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B1%87%E0%B0%97%E0%B0%82" title="వేగం — Telugu" lang="te" hreflang="te" data-title="వేగం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A1%D1%83%D1%80%D1%8A%D0%B0%D1%82" title="Суръат — Tađik" lang="tg" hreflang="tg" data-title="Суръат" data-language-autonym="Тоҷикӣ" data-language-local-name="Tađik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B9%80%E0%B8%A3%E0%B9%87%E0%B8%A7" title="ความเร็ว — Tajlandski" lang="th" hreflang="th" data-title="ความเร็ว" data-language-autonym="ไทย" data-language-local-name="Tajlandski" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Tulin" title="Tulin — Tagalski" lang="tl" hreflang="tl" data-title="Tulin" data-language-autonym="Tagalog" data-language-local-name="Tagalski" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/H%C4%B1z" title="Hız — Turski" lang="tr" hreflang="tr" data-title="Hız" data-language-autonym="Türkçe" data-language-local-name="Turski" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A2%D0%B8%D0%B7%D0%BB%D0%B5%D0%BA" title="Тизлек — Tatarski" lang="tt" hreflang="tt" data-title="Тизлек" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatarski" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A8%D0%B2%D0%B8%D0%B4%D0%BA%D1%96%D1%81%D1%82%D1%8C" title="Швидкість — Ukrajinski" lang="uk" hreflang="uk" data-title="Швидкість" data-language-autonym="Українська" data-language-local-name="Ukrajinski" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%88%D9%84%D8%A7%D8%B3%D9%B9%DB%8C" title="ولاسٹی — Urdu" lang="ur" hreflang="ur" data-title="ولاسٹی" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Tezlik" title="Tezlik — Uzbečki" lang="uz" hreflang="uz" data-title="Tezlik" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbečki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Piguz" title="Piguz — Veps" lang="vep" hreflang="vep" data-title="Piguz" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/V%E1%BA%ADn_t%E1%BB%91c" title="Vận tốc — Vijetnamski" lang="vi" hreflang="vi" data-title="Vận tốc" data-language-autonym="Tiếng Việt" data-language-local-name="Vijetnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Belosidad" title="Belosidad — Varej" lang="war" hreflang="war" data-title="Belosidad" data-language-autonym="Winaray" data-language-local-name="Varej" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%80%9F%E5%BA%A6" title="速度 — Wu kineski" lang="wuu" hreflang="wuu" data-title="速度" data-language-autonym="吴语" data-language-local-name="Wu kineski" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-velocity" title="I-velocity — Khosa" lang="xh" hreflang="xh" data-title="I-velocity" data-language-autonym="IsiXhosa" data-language-local-name="Khosa" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%92%D7%99%D7%9B%D7%A7%D7%99%D7%99%D7%98" title="גיכקייט — Jidiš" lang="yi" hreflang="yi" data-title="גיכקייט" data-language-autonym="ייִדיש" data-language-local-name="Jidiš" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%80%9F%E5%BA%A6" title="速度 — Kineski" lang="zh" hreflang="zh" data-title="速度" data-language-autonym="中文" data-language-local-name="Kineski" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E9%80%9F%E5%BA%A6" title="速度 — Literary Chinese" lang="lzh" hreflang="lzh" data-title="速度" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Sok-t%C5%8D%CD%98" title="Sok-tō͘ — min nan kineski" lang="nan" hreflang="nan" data-title="Sok-tō͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan kineski" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%80%9F%E5%BA%A6" title="速度 — kantonski" lang="yue" hreflang="yue" data-title="速度" data-language-autonym="粵語" data-language-local-name="kantonski" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11465#sitelinks-wikipedia" title="Uredi međujezične poveznice" class="wbc-editpage">Uredi 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stavku u skladištu podataka [g]" accesskey="g"><span>Stavka na Wikipodacima</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Pomagala"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Izgled"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Izgled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">premjesti na bočnu traku</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sakrij</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Izvor: Wikipedija</div> </div> <div id="contentSub" lang="sh-Latn" dir="ltr"><div id="mw-content-subtitle" lang="sh-Latn" dir="ltr"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sh-Latn" dir="ltr"><p><b>Brzina</b> (<a href="/wiki/Engleski_jezik" title="Engleski jezik">engl.</a> <i><span lang="en">velocity</span></i>; SI oznaka — <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9235b8758923fb5d7b4ad52d433544b41163d6ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.363ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}}"></span>) je prvi izvod <a href="/wiki/Vektor_pomeraja" class="mw-redirect" title="Vektor pomeraja">vektora položaja</a> materijalne tačke, čestice, ili tela u <a href="/wiki/Prostor" title="Prostor">prostoru</a> po vremenu. Predstavlja važan koncept u <a href="/wiki/Kinematika" title="Kinematika">kinematici</a> (jednoj od grana <a href="/wiki/Klasi%C4%8Dna_mehanika" title="Klasična mehanika">klasične mehanike</a>), koja opisuje samo <i>kako</i> se tela kreću, ne razmatrajući <i>zašto</i>, od. uzrok kretanja tela (čime se bavi <a href="/wiki/Dinamika_(fizika)" title="Dinamika (fizika)">dinamika</a>). </p><p>Brzina je <a href="/wiki/Vektor" title="Vektor">vektorska</a> <a href="/wiki/Fizi%C4%8Dka_veli%C4%8Dina" title="Fizička veličina">fizička veličina</a>: definisana je i intenzitetom/jačinom/magnitudom i smerom. <a href="/wiki/Apsolutna_vrednost" class="mw-redirect" title="Apsolutna vrednost">Apsolutna vrednost</a> brzine predstavlja njenu <a href="/wiki/Skalar_(matematika)" title="Skalar (matematika)">skalarnu</a> vrednost, tj. intenzitet; ovaj intenzitet se naziva <i>trenutnom putnom brzinom</i> (<a href="/wiki/Engleski_jezik" title="Engleski jezik">engl.</a> <i><span lang="en">instantaneous speed</span></i>) — fizička veličina čija je <a href="/wiki/SI" class="mw-redirect" title="SI">SI</a> jedinica <a href="/wiki/Metar_u_sekundi" title="Metar u sekundi">metar u sekundi</a> (oznaka: m/s ili m·s<sup>−1</sup>). Na primer, ako se kaže samo „5 metara u sekundi” dobija se vrednost <a href="/wiki/Skalar_(matematika)" title="Skalar (matematika)">skalara</a> (ne vektora), dok „5 metara u sekundi istočno” označava <a href="/wiki/Vektor" title="Vektor">vektor</a>. </p><p>Ukoliko postoji promena intenziteta i/ili smera brzine, za <a href="/wiki/Materijalna_ta%C4%8Dka" class="mw-redirect" title="Materijalna tačka">materijalnu tačku</a> koje podleže takvim promenama se kaže da je podvrgnuta <i><a href="/wiki/Ubrzanje" title="Ubrzanje">ubrzanju</a></i> i da se kreće <i>neravnomerno</i> (neravnomernom/promenljivom brzinom). </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Terminologija">Terminologija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=1" title="Uredi odjeljak Terminologija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=1" title="Uredi kôd odjeljka Terminologija"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pojam <i>brzina</i> u najširem smislu označava promenu neke veličine u jedinici vremena. U užem smislu (u fizici), brzina je prvi izvod vektora položaja materijalne tačke po vremenu. Dakle, ako se ne naglasi tačno o kojoj veličini se radi, podrazumeva se da je u pitanju <a href="/wiki/Fizi%C4%8Dka_veli%C4%8Dina" title="Fizička veličina">fizička veličina</a>. </p><p>Međutim, pojam <i>brzine</i> može da se definiše za svaku promenu tokom vremena i tada treba da se naglasi na koji se proces — ili veličinu — posmatrana brzina odnosi. Na primer: brzina <a href="/wiki/Hemijska_reakcija" title="Hemijska reakcija">hemijske reakcije</a> označava koliko se menja <a href="/wiki/Koncentracija" title="Koncentracija">koncentracija</a> <a href="/w/index.php?title=Reaktant&action=edit&redlink=1" class="new" title="Reaktant (stranica ne postoji)">reaktanata</a> ili <a href="/wiki/Produkt_(hemija)" title="Produkt (hemija)">produkata</a> u jedinici vremena; brzina radioaktivnog raspada (npr. <a href="/wiki/Alfa-raspad" class="mw-redirect" title="Alfa-raspad">alfa-raspad</a>) označava koliki se broj <a href="/wiki/Atomsko_jezgro" title="Atomsko jezgro">atomskih jezgara</a> raspadne u jedinici vremena itd. </p><p>Kada se u fizici kaže samo <i>brzina</i> (<a href="/wiki/Engleski_jezik" title="Engleski jezik">engl.</a> <i><span lang="en">velocity</span></i>) misli se isključivo na <i>trenutnu brzinu</i> (<a href="/wiki/Engleski_jezik" title="Engleski jezik">engl.</a> <i><span lang="en">instantaneous velocity</span></i>), dok se za samu <i>trenutnu brzinu</i>, te <i>srednju brzinu</i> (<a href="/wiki/Engleski_jezik" title="Engleski jezik">engl.</a> <i><span lang="en">average velocity</span></i>), <i>trenutnu putnu brzinu</i> (<a href="/wiki/Engleski_jezik" title="Engleski jezik">engl.</a> <i><span lang="en">instantaneous speed</span></i>), <i>srednju putnu brzinu</i> (<a href="/wiki/Engleski_jezik" title="Engleski jezik">engl.</a> <i><span lang="en">average speed</span></i>) i dr. moraju koristiti puni nazivi kako bi se ti pojmovi sa apsolutno različitim značenjima razlikovali. U kolokvijalnom govoru se za prethodno spomenute nazive uglavnom kaže samo — <i>brzina</i>, ili se isti pogrešno koriste kao <a href="/wiki/Sinonim" title="Sinonim">sinonimi</a> (slično kao i sa pojmovima <i><a href="/wiki/Masa" title="Masa">masa</a></i> i <i><a href="/wiki/Te%C5%BEina" title="Težina">težina</a></i>). </p> <div class="mw-heading mw-heading2"><h2 id="Konstantna_brzina">Konstantna brzina</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=2" title="Uredi odjeljak Konstantna brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=2" title="Uredi kôd odjeljka Konstantna brzina"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Materijalna_ta%C4%8Dka" class="mw-redirect" title="Materijalna tačka">Materijalna tačka</a> se na vremenskom intervalu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t=\left[t_{1},t_{2}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>=</mo> <mrow> <mo>[</mo> <mrow> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t=\left[t_{1},t_{2}\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f04358cd04a98785d5f0dcd955d5b7f1527baa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.989ex; height:2.843ex;" alt="{\displaystyle \Delta t=\left[t_{1},t_{2}\right]}"></span> kreće konstantnom brzinom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v_{const.}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold-italic">v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">c</mi> <mi mathvariant="bold-italic">o</mi> <mi mathvariant="bold-italic">n</mi> <mi mathvariant="bold-italic">s</mi> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold">.</mo> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v_{const.}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30819e678e3a54c162b51b5ee14c3c5435b8a1bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.607ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {v_{const.}}}}"></span> ukoliko se niti intenzitet niti smer te brzine tokom intervala, od. između trenutaka <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb0768c0bd659f2f84fb5ef9f4b74f336123d915" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{1}}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/749fee708b41e7079eabd50d61c8bf3e965db16f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{2}}"></span>, ne menjaju, tj. ukoliko se „kreće trenutnom brzinom” koja je za sve trenutke intervala jednaka (ima isti intenzitet i smer). </p> <div class="mw-heading mw-heading3"><h3 id="Konstantna_brzina_ili_ubrzanje">Konstantna brzina ili ubrzanje</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=3" title="Uredi odjeljak Konstantna brzina ili ubrzanje" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=3" title="Uredi kôd odjeljka Konstantna brzina ili ubrzanje"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Da bi telo u određenom vremenskom intervalu imalo konstantnu brzinu, mora imati konstantnu trenutnu putnu brzinu i kretati se u konstantnom smeru. Konstantan smer uslovljava telo na pravolinijsko kretanje (telo ne skreće, kreće se po jednom pravcu). Time se telo u određenom vremenskom intervalu kreće konstantnom brzinom samo ako je u tom intervalu kretanje po pravoj liniji i ako se trenutna putna brzina tokom intervala ne menja (jednaka je srednjoj putnoj brzini). </p><p>Na primer, automobil koji se kreće „konstantnom brzinom” od 20 kilometara na sat po kružnoj putanji može da ima konstantnu samo trenutnu putnu brzinu (jednaku srednjoj putnoj brzini), ali ne i trenutnu brzinu, jer se smer kretanja tokom obilaska kružnice menja (i to konstantno). Time se može zaključiti da se automobil ustvari ne kreće konstantnom brzinom već je podvrgnut ubrzanju (<a href="/wiki/Ubrzanje" title="Ubrzanje">centripetalno ubrzanje</a>) iako je trenutna putna brzina tokom kretanja bila konstantna. </p> <div class="mw-heading mw-heading2"><h2 id="Trenutna_brzina_i_trenutna_putna_brzina">Trenutna brzina i trenutna putna brzina</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=4" title="Uredi odjeljak Trenutna brzina i trenutna putna brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=4" title="Uredi kôd odjeljka Trenutna brzina i trenutna putna brzina"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Trenutna_brzina">Trenutna brzina</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=5" title="Uredi odjeljak Trenutna brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=5" title="Uredi kôd odjeljka Trenutna brzina"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Trenutna brzina <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9235b8758923fb5d7b4ad52d433544b41163d6ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.363ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}}"></span> je srednja brzina tokom beskonačno malog vremenskog intervala. Jednaka je prvom izvodu <a href="/wiki/Vektor_polo%C5%BEaja" class="mw-redirect" title="Vektor položaja">vektora položaja</a> (ne <a href="/wiki/Vektor_pomeraja" class="mw-redirect" title="Vektor pomeraja">vektora pomeraja</a>) materijalne tačke po vremenu: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}={\frac {d{\boldsymbol {\vec {r}}}}{d{\mathit {t}}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}={\frac {d{\boldsymbol {\vec {r}}}}{d{\mathit {t}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be557ffa8c92b5da11d171c426d24fe7de608572" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.567ex; height:5.676ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}={\frac {d{\boldsymbol {\vec {r}}}}{d{\mathit {t}}}},}"></span></dd></dl> <p>gde je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9235b8758923fb5d7b4ad52d433544b41163d6ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.363ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}}"></span> trenutna brzina u trenutku <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathit {t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathit {t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/612ac3d3706229e7ce66b5a6b22d0e09820d28a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.095ex; width:0.867ex; height:2.009ex;" alt="{\displaystyle {\mathit {t}}}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {r}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {r}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac8a6c987cd2becc815131033ed1f3872bd7dd74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.407ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {\vec {r}}}}"></span> vektor položaja materijalne tačke u tom istom trenutku. Ova relacija definiše trenutnu brzinu <a href="/wiki/Materijalna_ta%C4%8Dka" class="mw-redirect" title="Materijalna tačka">materijalne tačke</a>, čestice, ili tela, u bilo kojem određenom trenutku. Kako se koncept trenutne brzine na prvi pogled čini pomalo <i>neintuitivnim</i>, najbolje ga je razumeti tako da označava brzinu kojom bi se materijalna tačka koje ubrzava nastavila kretati ukoliko joj brzina u određenom trenutku postane konstantna. </p> <div class="mw-heading mw-heading3"><h3 id="Trenutna_putna_brzina">Trenutna putna brzina</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=6" title="Uredi odjeljak Trenutna putna brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=6" title="Uredi kôd odjeljka Trenutna putna brzina"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Trenutna putna brzina (veoma retko <i>u upotrebi</i>) <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{pt.}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <mo>.</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{pt.}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1dc7d55d716f1d72bfa1aac1329d7272338b26e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.428ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {v}}_{pt.}}"></span> je jednaka <a href="/wiki/Apsolutna_vrednost" class="mw-redirect" title="Apsolutna vrednost">apsolutnoj vrednosti</a>, od. intenzitetu trenutne brzine (prvog izvoda <a href="/wiki/Vektor_polo%C5%BEaja" class="mw-redirect" title="Vektor položaja">vektora položaja</a> po vremenu), zato što pređeni put i intenzitet <a href="/wiki/Vektor_pomeraja" class="mw-redirect" title="Vektor pomeraja">vektora pomeraja</a> (kada isti teže u nulu) postaju jednaki: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{pt.}=\left|{\boldsymbol {\vec {v}}}\,\right\vert =\left|{\frac {d{\boldsymbol {\vec {r}}}}{d{\mathit {t}}}}\right\vert ={\frac {d}{d{\mathit {t}}}}\left[{\frac {\boldsymbol {\vec {r}}}{\hat {r}}}\right]={\frac {d{\boldsymbol {r}}}{d{\mathit {t}}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <mo>.</mo> </mrow> </msub> <mo>=</mo> <mrow> <mo>|</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> </mrow> </mrow> </mrow> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{pt.}=\left|{\boldsymbol {\vec {v}}}\,\right\vert =\left|{\frac {d{\boldsymbol {\vec {r}}}}{d{\mathit {t}}}}\right\vert ={\frac {d}{d{\mathit {t}}}}\left[{\frac {\boldsymbol {\vec {r}}}{\hat {r}}}\right]={\frac {d{\boldsymbol {r}}}{d{\mathit {t}}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9593c7e1e58f7895f60b8d8583001e3824326275" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:35.457ex; height:6.176ex;" alt="{\displaystyle {\boldsymbol {v}}_{pt.}=\left|{\boldsymbol {\vec {v}}}\,\right\vert =\left|{\frac {d{\boldsymbol {\vec {r}}}}{d{\mathit {t}}}}\right\vert ={\frac {d}{d{\mathit {t}}}}\left[{\frac {\boldsymbol {\vec {r}}}{\hat {r}}}\right]={\frac {d{\boldsymbol {r}}}{d{\mathit {t}}}}.}"></span></dd></dl> <p>Trenutna putna brzina se može smatrati nagibom/gradijentom <a href="/wiki/Tangenta" title="Tangenta">tangente</a> na <a href="/wiki/Parabola" title="Parabola">parabolu</a> grafika zavisnosti <a href="/wiki/Polo%C5%BEaj" class="mw-redirect" title="Položaj">položaja</a> tela od vremena (<i>r</i>-<i>t</i> grafik): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{pt.}=\lim _{\Delta t\to 0}{\Delta {\boldsymbol {r}} \over \Delta t}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <mo>.</mo> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{pt.}=\lim _{\Delta t\to 0}{\Delta {\boldsymbol {r}} \over \Delta t}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bcfe928824e5227727e81611ce10fa6a687d6bb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.99ex; height:5.676ex;" alt="{\displaystyle {\boldsymbol {v}}_{pt.}=\lim _{\Delta t\to 0}{\Delta {\boldsymbol {r}} \over \Delta t}.}"></span></dd></dl> <p>Kako je koeficijent <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{f(x)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{f(x)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b83d3f3ad95d2cc6630d4a7489ebe86c4e01ea2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:4.567ex; height:3.009ex;" alt="{\displaystyle k_{f(x)}}"></span> nagiba <a href="/wiki/Tangenta" title="Tangenta">tangente</a> na grafik funkcije <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.418ex; height:2.843ex;" alt="{\displaystyle f(x)}"></span> nultog ili prvog stepena (<a href="/w/index.php?title=Linearna_funkcija&action=edit&redlink=1" class="new" title="Linearna funkcija (stranica ne postoji)">linearne funkcije</a>) — na liniju — nagib te linije, isti se može posmatrati i kao nagib <a href="/wiki/Du%C5%BE" title="Duž">duži</a> ograničene dvema tačkama koordinata (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8788bf85d532fa88d1fb25eff6ae382a601c308" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{1}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af71fd012905bda20f1c736716748676d67c93f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.472ex; height:2.843ex;" alt="{\displaystyle f(x_{1})}"></span>) i <br />(<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7af1b928f06e4c7e3e8ebfd60704656719bd766" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.384ex; height:2.009ex;" alt="{\displaystyle x_{2}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c20b8a11295ef90324bb4ece6fe2a3dbb6ac996" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.472ex; height:2.843ex;" alt="{\displaystyle f(x_{2})}"></span>), i jednak je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{f(x)}={\frac {f(x_{2})-f(x_{1})}{x_{2}-x_{1}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−</mo> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{f(x)}={\frac {f(x_{2})-f(x_{1})}{x_{2}-x_{1}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4dc28a15100c70beda7c6dc9ed58e5d3a6dcccdd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:22.933ex; height:6.009ex;" alt="{\displaystyle k_{f(x)}={\frac {f(x_{2})-f(x_{1})}{x_{2}-x_{1}}},}"></span></dd></dl> <p>tako je koeficijent <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{f'(x)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{f'(x)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe451cc9641216a31ca132f7b5384079c7dc8164" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:4.61ex; height:3.176ex;" alt="{\displaystyle l_{f'(x)}}"></span> nagiba tangente na grafik funkcije <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f'(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f'(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0cd7d7c75340e779d82658e19d1720ce84ab127" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.144ex; height:3.009ex;" alt="{\displaystyle f'(x)}"></span> drugog ili višeg stepena (<a href="/wiki/Kvadratna_jedna%C4%8Dina" title="Kvadratna jednačina">kvadratne</a>, kubne i dr. funkcije) — na <a href="/wiki/Parabola" title="Parabola">parabolu</a> — u tački koordinata (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f'(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f'(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0cd7d7c75340e779d82658e19d1720ce84ab127" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.144ex; height:3.009ex;" alt="{\displaystyle f'(x)}"></span>) jednak: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{f'(x)}=\lim _{\Delta x\to 0}{f'(x+\Delta x)-f'(x) \over \Delta x}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{f'(x)}=\lim _{\Delta x\to 0}{f'(x+\Delta x)-f'(x) \over \Delta x}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d16153f58751dfeec2bc4d56e32f769a8f24acc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:33.588ex; height:6.009ex;" alt="{\displaystyle l_{f'(x)}=\lim _{\Delta x\to 0}{f'(x+\Delta x)-f'(x) \over \Delta x}.}"></span></dd></dl> <p>Ako se za primer uzme <a href="/wiki/Funkcija_(matematika)" class="mw-redirect" title="Funkcija (matematika)">funkcija</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r(t)=t^{3}+2t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r(t)=t^{3}+2t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ed03be4ce7a02bb212708643d110a4730a86deb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.532ex; height:3.176ex;" alt="{\displaystyle r(t)=t^{3}+2t}"></span> nagib <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{r(t)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{r(t)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65b096bebb35208c209939bbf2b05dbe92cc8ebb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:3.54ex; height:3.009ex;" alt="{\displaystyle l_{r(t)}}"></span> bi bio: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{(t+\Delta t)^{3}+2(t+\Delta t)-(t^{3}+2t) \over \Delta t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo stretchy="false">(</mo> <mi>t</mi> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mo stretchy="false">(</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{(t+\Delta t)^{3}+2(t+\Delta t)-(t^{3}+2t) \over \Delta t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f0091a891003358a1c6e7ce6a2fe48244fd8a8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:45.262ex; height:6.176ex;" alt="{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{(t+\Delta t)^{3}+2(t+\Delta t)-(t^{3}+2t) \over \Delta t}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{t^{3}+3t^{2}\Delta t+3t{\Delta t}^{2}+{\Delta t}^{3}+2t+2\Delta t-t^{3}-2t \over \Delta t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>3</mn> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>+</mo> <mn>3</mn> <mi>t</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>2</mn> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>−</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mi>t</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{t^{3}+3t^{2}\Delta t+3t{\Delta t}^{2}+{\Delta t}^{3}+2t+2\Delta t-t^{3}-2t \over \Delta t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cc24efae3f422e792762fd15ba21a3eaaf564c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:59.395ex; height:6.176ex;" alt="{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{t^{3}+3t^{2}\Delta t+3t{\Delta t}^{2}+{\Delta t}^{3}+2t+2\Delta t-t^{3}-2t \over \Delta t}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{3t^{2}\Delta t+3t{\Delta t}^{2}+{\Delta t}^{3}+2\Delta t \over \Delta t}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>3</mn> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>+</mo> <mn>3</mn> <mi>t</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{3t^{2}\Delta t+3t{\Delta t}^{2}+{\Delta t}^{3}+2\Delta t \over \Delta t}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce15212423ac571f10b6a0bc9c6be1827df55de4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:40.242ex; height:6.176ex;" alt="{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{3t^{2}\Delta t+3t{\Delta t}^{2}+{\Delta t}^{3}+2\Delta t \over \Delta t}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{3t^{2}+3t\Delta t+{\Delta t}^{2}+2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>3</mn> <mi>t</mi> <mi mathvariant="normal">Δ</mi> <mi>t</mi> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{3t^{2}+3t\Delta t+{\Delta t}^{2}+2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74578f8c3e655290a05a9f181e5c0b70fa94cf6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:32.801ex; height:4.509ex;" alt="{\displaystyle l_{r(t)}=\lim _{\Delta t\to 0}{3t^{2}+3t\Delta t+{\Delta t}^{2}+2}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{r(t)}=3t^{2}+2.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <mn>3</mn> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{r(t)}=3t^{2}+2.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d196da88ac57b7a492401115072d34bb90276a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:14.345ex; height:3.509ex;" alt="{\displaystyle l_{r(t)}=3t^{2}+2.}"></span></dd></dl> <p>Dobijeno rešenje <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l_{r(t)}=3t^{2}+2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>=</mo> <mn>3</mn> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l_{r(t)}=3t^{2}+2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97f18cfd3376a99c0b2b9fac11e1e3c1fb51a05b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:13.698ex; height:3.509ex;" alt="{\displaystyle l_{r(t)}=3t^{2}+2}"></span>  je ustvari trenutna putna brzina tela (ne uzimajući u obzir merne jedinice) čiji se položaj u zavisnosti od vremena menja kao <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r(t)=t^{3}+2t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r(t)=t^{3}+2t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ed03be4ce7a02bb212708643d110a4730a86deb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.532ex; height:3.176ex;" alt="{\displaystyle r(t)=t^{3}+2t}"></span>, u trenutku <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>, i predstavlja <a href="/wiki/Izvod" title="Izvod">izvod</a> funkcije položaja tog tela u zavisnosti od vremena upravo po vremenu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span>, što bi se — ako u obzir uzmemo i merne jedinice — moglo izraziti kao: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{pt.}={\frac {d}{d{\mathit {t}}}}\left[r(t)\right]={\frac {d}{d{\mathit {t}}}}\left[t^{3}\,\mathrm {ms^{-3}} +2t\,\mathrm {ms^{-1}} \right]=3t^{2}\,\mathrm {ms^{-3}} +2\cdot 1t^{0}\,\mathrm {ms^{-1}} =3t^{2}\,\mathrm {ms^{-3}} +2\,\mathrm {ms^{-1}} =l_{r(t)}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <mo>.</mo> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> </mrow> </mrow> </mrow> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">t</mi> </mrow> </mrow> </mrow> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mi>t</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mrow> <mo>]</mo> </mrow> <mo>=</mo> <mn>3</mn> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mo>⋅</mo> <mn>1</mn> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo>=</mo> <mn>3</mn> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> <mo>+</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <msup> <mi mathvariant="normal">s</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo>=</mo> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{pt.}={\frac {d}{d{\mathit {t}}}}\left[r(t)\right]={\frac {d}{d{\mathit {t}}}}\left[t^{3}\,\mathrm {ms^{-3}} +2t\,\mathrm {ms^{-1}} \right]=3t^{2}\,\mathrm {ms^{-3}} +2\cdot 1t^{0}\,\mathrm {ms^{-1}} =3t^{2}\,\mathrm {ms^{-3}} +2\,\mathrm {ms^{-1}} =l_{r(t)}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb39c564bf597e76901bc808d4f84a730056d7f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:95.293ex; height:5.509ex;" alt="{\displaystyle v_{pt.}={\frac {d}{d{\mathit {t}}}}\left[r(t)\right]={\frac {d}{d{\mathit {t}}}}\left[t^{3}\,\mathrm {ms^{-3}} +2t\,\mathrm {ms^{-1}} \right]=3t^{2}\,\mathrm {ms^{-3}} +2\cdot 1t^{0}\,\mathrm {ms^{-1}} =3t^{2}\,\mathrm {ms^{-3}} +2\,\mathrm {ms^{-1}} =l_{r(t)}.}"></span></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Razlika_između_trenutne_brzine_i_trenutne_putne_brzine"><span id="Razlika_izme.C4.91u_trenutne_brzine_i_trenutne_putne_brzine"></span>Razlika između trenutne brzine i trenutne putne brzine</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=7" title="Uredi odjeljak Razlika između trenutne brzine i trenutne putne brzine" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=7" title="Uredi kôd odjeljka Razlika između trenutne brzine i trenutne putne brzine"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Trenutna putna brzina opisuje koliko brzo telo menja svoj <a href="/wiki/Polo%C5%BEaj" class="mw-redirect" title="Položaj">položaj</a> u određenom trenutku nezavisno od smera kretanja, dok trenutna brzina opisuje koliko brzo telo menja svoj <a href="/wiki/Vektor_polo%C5%BEaja" class="mw-redirect" title="Vektor položaja">vektor položaja</a> u određenom trenutku (daje i smer u kojem se promena vektora položaja dešava). Ukoliko se za automobl kaže da u određenom trenutku „putuje 60 km/h”, time mu je određena samo trenutna putna brzina. S druge strane, ukoliko se kaže da automobil „putuje 60 km/h prema severu”, tada je definisana i trenutna brzina automobila i trenutna putna brzina. </p> <div class="mw-heading mw-heading2"><h2 id="Srednja_brzina_i_srednja_putna_brzina">Srednja brzina i srednja putna brzina</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=8" title="Uredi odjeljak Srednja brzina i srednja putna brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=8" title="Uredi kôd odjeljka Srednja brzina i srednja putna brzina"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Srednja_brzina">Srednja brzina</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=9" title="Uredi odjeljak Srednja brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=9" title="Uredi kôd odjeljka Srednja brzina"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Srednja brzina <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle {\boldsymbol {\vec {v}}}\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle {\boldsymbol {\vec {v}}}\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28c2ebcc2c8cf15706a536b4f79710f321fb3fe4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.172ex; height:2.843ex;" alt="{\displaystyle \langle {\boldsymbol {\vec {v}}}\rangle }"></span> je konstantna brzina kojom bi <a href="/wiki/Materijalna_ta%C4%8Dka" class="mw-redirect" title="Materijalna tačka">materijalna tačka</a> trebalo da se kreće da bi ostvarila isti <a href="/wiki/Pomeraj" title="Pomeraj">vektor pomeraja</a> kao kod kretanja promenljivom brzinom, u određenom (istom) vremenskom intervalu. Jednaka je količniku <a href="/wiki/Pomeraj" title="Pomeraj">vektora pomeraja</a> i proteklog vremena za koji je ostvaren: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle {\boldsymbol {\vec {v}}}\rangle ={\frac {\Delta {\boldsymbol {\vec {r}}}}{\Delta t}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle {\boldsymbol {\vec {v}}}\rangle ={\frac {\Delta {\boldsymbol {\vec {r}}}}{\Delta t}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4278d314f127c758d692f1bbeb809212146aa27f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.096ex; height:5.676ex;" alt="{\displaystyle \langle {\boldsymbol {\vec {v}}}\rangle ={\frac {\Delta {\boldsymbol {\vec {r}}}}{\Delta t}}.}"></span></dd></dl> <p>Srednja brzina na intervalu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c28867ecd34e2caed12cf38feadf6a81a7ee542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.775ex; height:2.176ex;" alt="{\displaystyle \Delta t}"></span> se može smatrati tetivom između dveju tačaka sa <i>x</i>-koordinatama <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb0768c0bd659f2f84fb5ef9f4b74f336123d915" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{1}}"></span> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/749fee708b41e7079eabd50d61c8bf3e965db16f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.894ex; height:2.343ex;" alt="{\displaystyle t_{2}}"></span> koje određuju granice intervala za koji se srednja brzina računa. </p><p>Bitna stvar za naglasiti je da se reč <i>srednja</i> ne meša sa pojmom <i>srednja vrednost</i> ili <i>prosek</i>, jer <i>srednja brzina</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86b443aa5832287af231578153c8ac8d166a9786" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.719ex; height:3.009ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}"></span> na intervalu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82bf7d02950370ebff85cc4f0b36cb235b40adb6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:30.342ex; height:2.509ex;" alt="{\displaystyle \Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}"></span> ne označava <i>srednju vrednost srednje brzine</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>r</mi> <msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d1786ae8c5fd7440a5e3a1911b15a6ab6ba898c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:19.883ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {v}}_{sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"></span> (<i>prosečnu srednju brzinu</i>) sa <i>n</i> vremenskih intervala, već označava količnik rezultujućeg vektora pomeraja <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {r}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {r}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4728c609ac035347c766da80471ce9c4ccbc366" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.763ex; height:3.009ex;" alt="{\displaystyle {\boldsymbol {\vec {r}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}"></span> (na <i>n</i> prethodno spomenutih intervala) i jednog vremenskog intervala <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t_{u}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t_{u}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96edfe275b60b142bc6e2c5d996065d6c7705e5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.948ex; height:2.509ex;" alt="{\displaystyle \Delta t_{u}}"></span> (koji bi predstavljao zbir svih prethodno spomenutih <i>n</i> intervala). Do zabune može doći ukoliko se umesto naziva <i>srednja brzina</i> koristi naziv <i>brzina</i>; tada bi <i>srednja vrednost srednje brzine</i> (<i>prosečna srednja brzina</i>) imala naziv <i>srednja brzina</i> (ili <i>prosečna brzina</i>): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}_{sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}={\frac {{\boldsymbol {\vec {v}}}_{\Delta t_{1}}+{\boldsymbol {\vec {v}}}_{\Delta t_{2}}+{\boldsymbol {\vec {v}}}_{\Delta t_{3}}+\,\cdots \,+{\boldsymbol {\vec {v}}}_{\Delta t_{n}}}{n}}={\frac {{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{1}}}{\Delta t_{1}}}+{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{2}}}{\Delta t_{2}}}+{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{3}}}{\Delta t_{3}}}+\,\cdots \,+{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{n}}}{\Delta t_{n}}}}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>r</mi> <msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mrow> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}_{sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}={\frac {{\boldsymbol {\vec {v}}}_{\Delta t_{1}}+{\boldsymbol {\vec {v}}}_{\Delta t_{2}}+{\boldsymbol {\vec {v}}}_{\Delta t_{3}}+\,\cdots \,+{\boldsymbol {\vec {v}}}_{\Delta t_{n}}}{n}}={\frac {{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{1}}}{\Delta t_{1}}}+{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{2}}}{\Delta t_{2}}}+{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{3}}}{\Delta t_{3}}}+\,\cdots \,+{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{n}}}{\Delta t_{n}}}}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e29e225de9d4e7c1ce05f17c862408a6187f6c9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:93.069ex; height:8.176ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}_{sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}={\frac {{\boldsymbol {\vec {v}}}_{\Delta t_{1}}+{\boldsymbol {\vec {v}}}_{\Delta t_{2}}+{\boldsymbol {\vec {v}}}_{\Delta t_{3}}+\,\cdots \,+{\boldsymbol {\vec {v}}}_{\Delta t_{n}}}{n}}={\frac {{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{1}}}{\Delta t_{1}}}+{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{2}}}{\Delta t_{2}}}+{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{3}}}{\Delta t_{3}}}+\,\cdots \,+{\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{n}}}{\Delta t_{n}}}}{n}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}={\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}{\Delta t_{u}}}={\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{1}}+{\boldsymbol {\vec {r}}}_{\Delta t_{2}}+{\boldsymbol {\vec {r}}}_{\Delta t_{3}}+\,\cdots \,+{\boldsymbol {\vec {r}}}_{\Delta t_{n}}}{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}={\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}{\Delta t_{u}}}={\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{1}}+{\boldsymbol {\vec {r}}}_{\Delta t_{2}}+{\boldsymbol {\vec {r}}}_{\Delta t_{3}}+\,\cdots \,+{\boldsymbol {\vec {r}}}_{\Delta t_{n}}}{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01c55e6a0c317cc87609cb74c01d1a66775b3c81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:82.078ex; height:6.343ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}={\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}{\Delta t_{u}}}={\frac {{\boldsymbol {\vec {r}}}_{\Delta t_{1}}+{\boldsymbol {\vec {r}}}_{\Delta t_{2}}+{\boldsymbol {\vec {r}}}_{\Delta t_{3}}+\,\cdots \,+{\boldsymbol {\vec {r}}}_{\Delta t_{n}}}{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Srednja_putna_brzina">Srednja putna brzina</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=10" title="Uredi odjeljak Srednja putna brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=10" title="Uredi kôd odjeljka Srednja putna brzina"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Srednja putna brzina (ili, mnogo češće, samo — putna brzina) <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <mo>.</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ee2b8b16cdcaad008b176e6d6849db974eeca29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.238ex; height:3.009ex;" alt="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.}}"></span> je konstantna brzina kojom bi <a href="/wiki/Materijalna_ta%C4%8Dka" class="mw-redirect" title="Materijalna tačka">materijalna tačka</a> trebalo da se kreće da bi prešla isti put kao kod kretanja promenljivom brzinom, u određenom (istom) vremenskom intervalu. Jednaka je količniku ukupnog <a href="/wiki/Pre%C4%91eni_put" class="mw-redirect" title="Pređeni put">pređenog puta</a> i proteklog vremena za koji je pređen: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.}={\frac {{\boldsymbol {s}}_{u}}{\Delta t}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <mo>.</mo> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.}={\frac {{\boldsymbol {s}}_{u}}{\Delta t}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f53944f78a12039d790c3c95d06a64377ab1e86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.595ex; height:4.843ex;" alt="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.}={\frac {{\boldsymbol {s}}_{u}}{\Delta t}}.}"></span></dd></dl> <div class="mw-heading mw-heading4"><h4 id="Razlika_između_srednje_brzine_i_srednje_putne_brzine"><span id="Razlika_izme.C4.91u_srednje_brzine_i_srednje_putne_brzine"></span>Razlika između srednje brzine i srednje putne brzine</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=11" title="Uredi odjeljak Razlika između srednje brzine i srednje putne brzine" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=11" title="Uredi kôd odjeljka Razlika između srednje brzine i srednje putne brzine"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Velika razlika između između srednje brzine i srednje putne brzine se može primetiti ako se u obzir uzme kretanje po <a href="/wiki/Kru%C5%BEnica" title="Kružnica">kružnici</a>. Ukoliko se telo kreće po kružnici promenljivom trenutnom putnom brzinom (time je, automatski, uslovljena i promenljiva trenutna brzina (koja je kod kretanja po kružnici uvek promenljiva, što ne mora značiti da je istina i za trenutnu putnu brzinu, koja može biti konstantna ukoliko je jednaka srednjoj putnoj brzini (ukoliko je tangencijalno ubrzanje jednako 0), i koja predstavlja intenzitet trenutne brzine — <a href="/wiki/Skalar_(matematika)" title="Skalar (matematika)">skalar</a> je)), te nakon određenog vremenskog intervala — nakon što napravi jedan obrtaj — vrati u svoj početni položaj njegova srednja brzina na tom intervalu je jednaka nuli (srednja brzina označava kojom konstantnom brzinom (i u kojem smeru) bi se telo trebalo kretati da ostvari isti <a href="/wiki/Pomeraj" title="Pomeraj">vektor pomeraja</a> kao kod kretanja promenljivom brzinom, na određenom (istom) vremenskom intervalu), dok se srednja putna brzina tela moža naći deljenjem obima kruga (ukupnog <a href="/wiki/Pre%C4%91eni_put" class="mw-redirect" title="Pređeni put">pređenog puta</a>) sa dužinom vremenskog intervala (proteklim vremenom potrebnim da se ukupni put pređe). Ovo je tačno zato što se srednja brzina računa uzimajući u obzir razliku između krajnjeg i početnog <a href="/wiki/Vektor_polo%C5%BEaja" class="mw-redirect" title="Vektor položaja">vektora položaja</a> i ukupno vreme potrebno za promenu tog položaja, dok se za srednju putnu brzinu uzima ukupni <a href="/wiki/Pre%C4%91eni_put" class="mw-redirect" title="Pređeni put">pređeni put</a> i potrebno vreme da se taj put pređe. </p><p>Srednja brzina je po intenzitetu uvek manja ili jednaka srednjoj putnoj brzini tela. Ovo se može ustvrdeti shvaćanjem da dok se <a href="/wiki/Pre%C4%91eni_put" class="mw-redirect" title="Pređeni put">pređeni put</a> uvek striktno povećava, <a href="/wiki/Vektor_pomeraja" class="mw-redirect" title="Vektor pomeraja">vektor pomeraja</a> se može ili povećavati ili smanjivati. </p><p>Bitna stvar za naglasiti je da se reč <i>srednja</i> ne meša sa pojmom <i>srednja vrednost</i> ili <i>prosek</i>, jer <i>srednja putna brzina</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b131bea8ce89735de6a03b014659449e6fe29b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:21.601ex; height:3.509ex;" alt="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"></span> na intervalu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82bf7d02950370ebff85cc4f0b36cb235b40adb6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:30.342ex; height:2.509ex;" alt="{\displaystyle \Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}"></span> ne označava <i>srednju vrednost srednje putne brzine</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.\,sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <mo>.</mo> <mspace width="thinmathspace" /> <mi>s</mi> <mi>r</mi> <msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.\,sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab5928daa6c26278e716c41c3dc0e55423a86e2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:23.958ex; height:3.509ex;" alt="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.\,sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"></span> (<i>prosečnu srednju putnu brzinu</i>) sa <i>n</i> vremenskih intervala, već označava količnik ukupnog pređenog puta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {s}}_{u_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {s}}_{u_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f9eb57149975505bbf5ae79d9b217e6c05c0a9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:18.77ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {s}}_{u_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"></span> (na <i>n</i> prethodno spomenutih intervala) i jednog vremenskog intervala <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta t_{u}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta t_{u}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96edfe275b60b142bc6e2c5d996065d6c7705e5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.948ex; height:2.509ex;" alt="{\displaystyle \Delta t_{u}}"></span> (koji bi predstavljao zbir svih prethodno spomenutih <i>n</i> intervala). Do zabune može doći ukoliko se umesto naziva <i>srednja putna brzina</i> koristi naziv <i>putna brzina</i>; tada bi <i>srednja vrednost srednje putne brzine</i> (<i>prosečna srednja putna brzina</i>) imala naziv <i>srednja putna brzina</i> (ili <i>prosečna putna brzina</i>): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.\,sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}={\frac {\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{1}}}+\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{2}}}+\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{3}}}+\,\cdots \,\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{n}}}}{n}}={\frac {{\frac {{\boldsymbol {s}}_{u_{\Delta t_{1}}}}{\Delta t_{1}}}+{\frac {{\boldsymbol {s}}_{u_{\Delta t_{2}}}}{\Delta t_{2}}}+{\frac {{\boldsymbol {s}}_{u_{\Delta t_{3}}}}{\Delta t_{3}}}+\,\cdots \,+{\frac {{\boldsymbol {s}}_{u_{\Delta t_{n}}}}{\Delta t_{n}}}}{n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <mo>.</mo> <mspace width="thinmathspace" /> <mi>s</mi> <mi>r</mi> <msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mrow> <mi>n</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.\,sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}={\frac {\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{1}}}+\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{2}}}+\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{3}}}+\,\cdots \,\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{n}}}}{n}}={\frac {{\frac {{\boldsymbol {s}}_{u_{\Delta t_{1}}}}{\Delta t_{1}}}+{\frac {{\boldsymbol {s}}_{u_{\Delta t_{2}}}}{\Delta t_{2}}}+{\frac {{\boldsymbol {s}}_{u_{\Delta t_{3}}}}{\Delta t_{3}}}+\,\cdots \,+{\frac {{\boldsymbol {s}}_{u_{\Delta t_{n}}}}{\Delta t_{n}}}}{n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36be77b8f843ebb33cd589328a95a10ff65d70b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:111.197ex; height:7.676ex;" alt="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt.\,sr._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}={\frac {\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{1}}}+\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{2}}}+\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{3}}}+\,\cdots \,\langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{n}}}}{n}}={\frac {{\frac {{\boldsymbol {s}}_{u_{\Delta t_{1}}}}{\Delta t_{1}}}+{\frac {{\boldsymbol {s}}_{u_{\Delta t_{2}}}}{\Delta t_{2}}}+{\frac {{\boldsymbol {s}}_{u_{\Delta t_{3}}}}{\Delta t_{3}}}+\,\cdots \,+{\frac {{\boldsymbol {s}}_{u_{\Delta t_{n}}}}{\Delta t_{n}}}}{n}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}={\frac {{\boldsymbol {s}}_{u_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}{\Delta t_{u}}}={\frac {{\boldsymbol {s}}_{u_{\Delta t_{1}}}+{\boldsymbol {s}}_{u_{\Delta t_{2}}}+{\boldsymbol {s}}_{u_{\Delta t_{3}}}+\,\cdots \,+{\boldsymbol {s}}_{u_{\Delta t_{n}}}}{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>t</mi> <msub> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">s</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </msub> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>+</mo> <mspace width="thinmathspace" /> <mo>⋯</mo> <mspace width="thinmathspace" /> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}={\frac {{\boldsymbol {s}}_{u_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}{\Delta t_{u}}}={\frac {{\boldsymbol {s}}_{u_{\Delta t_{1}}}+{\boldsymbol {s}}_{u_{\Delta t_{2}}}+{\boldsymbol {s}}_{u_{\Delta t_{3}}}+\,\cdots \,+{\boldsymbol {s}}_{u_{\Delta t_{n}}}}{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e30e79d69dea12ce71d0a62ce7c1247f9e801c3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:83.093ex; height:6.343ex;" alt="{\displaystyle \langle {\boldsymbol {v}}\rangle _{pt._{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}={\frac {{\boldsymbol {s}}_{u_{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}{\Delta t_{u}}}={\frac {{\boldsymbol {s}}_{u_{\Delta t_{1}}}+{\boldsymbol {s}}_{u_{\Delta t_{2}}}+{\boldsymbol {s}}_{u_{\Delta t_{3}}}+\,\cdots \,+{\boldsymbol {s}}_{u_{\Delta t_{n}}}}{\Delta t_{1}+\Delta t_{2}+\Delta t_{3}+\,\cdots \,+\Delta t_{n}}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Jednačine_kretanja"><span id="Jedna.C4.8Dine_kretanja"></span>Jednačine kretanja</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=12" title="Uredi odjeljak Jednačine kretanja" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=12" title="Uredi kôd odjeljka Jednačine kretanja"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Konstantno_ubrzanje">Konstantno ubrzanje</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=13" title="Uredi odjeljak Konstantno ubrzanje" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=13" title="Uredi kôd odjeljka Konstantno ubrzanje"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>U posebnim slučajevima sa konstantnim <a href="/wiki/Ubrzanje" title="Ubrzanje">ubrzanjem</a>, trenutna brzina <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cd253caa73dbcc9561309d1f6649d87876fb2a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:3.747ex; height:3.176ex;" alt="{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}}"></span> se može računati jednačinama kretanja. Uzimajući <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {a}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {a}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2b416944a3b5a36660045dc05211d82069716fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.471ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {\vec {a}}}}"></span> za <a href="/wiki/Ubrzanje" title="Ubrzanje">ubrzanje</a> jednako nekom proizvoljnom konstantnom <a href="/wiki/Vektor" title="Vektor">vektoru</a> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {{\vec {v}}_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {{\vec {v}}_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd1094e1a10c4010bd3aea358e617c32519bb640" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.54ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {{\vec {v}}_{0}}}}"></span> za početnu brzinu kretanja u trenutku <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{0}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/129dee73708133aabd89cd4adf5f38ebcaf23a86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.155ex; height:2.509ex;" alt="{\displaystyle t_{0}=0}"></span> zavisnost trenutne brzine od vremena <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> je data kao: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}={\boldsymbol {{\vec {v}}_{0}}}+{\boldsymbol {\vec {a}}}\cdot t.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}={\boldsymbol {{\vec {v}}_{0}}}+{\boldsymbol {\vec {a}}}\cdot t.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/509efd82ea79f3deb9b4222caec3c3c1aa895f38" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:16.863ex; height:3.176ex;" alt="{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}={\boldsymbol {{\vec {v}}_{0}}}+{\boldsymbol {\vec {a}}}\cdot t.}"></span></dd></dl> <p>Kombinovanjem ove jednačine sa opštom jednačinom zavisnosti <a href="/wiki/Vektor_pomeraja" class="mw-redirect" title="Vektor pomeraja">vektora pomeraja</a> tela od vremena (uvrštavajući <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {a}}}={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-{\boldsymbol {{\vec {v}}_{0}}}}{t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mi>t</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {a}}}={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-{\boldsymbol {{\vec {v}}_{0}}}}{t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb553529518d665207de2b4b7439a5ceee6208ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.533ex; height:6.009ex;" alt="{\displaystyle {\boldsymbol {\vec {a}}}={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-{\boldsymbol {{\vec {v}}_{0}}}}{t}}}"></span> iz prethodne jednačine u istu): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {{\vec {r}}_{(t)}}}={\boldsymbol {{\vec {r}}_{0}}}+{\boldsymbol {{\vec {v}}_{0}}}\cdot t+{\frac {{\boldsymbol {\vec {a}}}\cdot t^{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mi>t</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {{\vec {r}}_{(t)}}}={\boldsymbol {{\vec {r}}_{0}}}+{\boldsymbol {{\vec {v}}_{0}}}\cdot t+{\frac {{\boldsymbol {\vec {a}}}\cdot t^{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94783640e3478d49a6e4d482f9716ac6b0a0a556" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:26.095ex; height:5.676ex;" alt="{\displaystyle {\boldsymbol {{\vec {r}}_{(t)}}}={\boldsymbol {{\vec {r}}_{0}}}+{\boldsymbol {{\vec {v}}_{0}}}\cdot t+{\frac {{\boldsymbol {\vec {a}}}\cdot t^{2}}{2}}}"></span></dd></dl> <p>moguće je povezati vektor pomeraja i srednju brzinu kao: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}+{\boldsymbol {{\vec {v}}_{0}}}}{2}}\cdot t=\langle {\boldsymbol {\vec {v}}}\,\rangle \cdot {t},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>⋅</mo> <mi>t</mi> <mo>=</mo> <mo fence="false" stretchy="false">⟨</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mo fence="false" stretchy="false">⟩</mo> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}+{\boldsymbol {{\vec {v}}_{0}}}}{2}}\cdot t=\langle {\boldsymbol {\vec {v}}}\,\rangle \cdot {t},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37a2ad69cf71a691d3c42e5e4e9a928d7d9b4705" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:31.131ex; height:6.009ex;" alt="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}+{\boldsymbol {{\vec {v}}_{0}}}}{2}}\cdot t=\langle {\boldsymbol {\vec {v}}}\,\rangle \cdot {t},}"></span></dd></dl> <p>koja je u ovom slučaju jednaka srednjoj vrednosti srednje brzine (proseku srednje brzine), od. srednjoj vrednosti (proseku) početne i krajnje brzine. </p><p>Takođe je moguće izvesti izraz za brzinu direktno nezavisan o vremenu i poznat pod imenom <a href="/w/index.php?title=Tori%C4%8Delijeva_jedna%C4%8Dina&action=edit&redlink=1" class="new" title="Toričelijeva jednačina (stranica ne postoji)">Toričelijeva jednačina</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}^{2}={\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}=({\boldsymbol {{\vec {v}}_{0}}}+{\boldsymbol {\vec {a}}}\cdot t)\cdot ({\boldsymbol {{\vec {v}}_{0}}}+{\boldsymbol {\vec {a}}}\cdot t)={\boldsymbol {{\vec {v}}_{0}}}^{2}+2\cdot t\cdot ({\boldsymbol {\vec {a}}}\cdot {\boldsymbol {{\vec {v}}_{0}}})+{\boldsymbol {\vec {a}}}\,^{2}\cdot t^{2}\ \ \ \Rightarrow \ \ \ {\boldsymbol {{\vec {v}}_{(t)}}}^{2}-\,{\boldsymbol {{\vec {v}}_{0}}}^{2}=2\cdot t\cdot ({\boldsymbol {\vec {a}}}\cdot {\boldsymbol {{\vec {v}}_{0}}})+{\boldsymbol {\vec {a}}}\,^{2}\cdot t^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo>⋅</mo> <mi>t</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mo stretchy="false">⇒</mo> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mspace width="thinmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mo>⋅</mo> <mi>t</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}^{2}={\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}=({\boldsymbol {{\vec {v}}_{0}}}+{\boldsymbol {\vec {a}}}\cdot t)\cdot ({\boldsymbol {{\vec {v}}_{0}}}+{\boldsymbol {\vec {a}}}\cdot t)={\boldsymbol {{\vec {v}}_{0}}}^{2}+2\cdot t\cdot ({\boldsymbol {\vec {a}}}\cdot {\boldsymbol {{\vec {v}}_{0}}})+{\boldsymbol {\vec {a}}}\,^{2}\cdot t^{2}\ \ \ \Rightarrow \ \ \ {\boldsymbol {{\vec {v}}_{(t)}}}^{2}-\,{\boldsymbol {{\vec {v}}_{0}}}^{2}=2\cdot t\cdot ({\boldsymbol {\vec {a}}}\cdot {\boldsymbol {{\vec {v}}_{0}}})+{\boldsymbol {\vec {a}}}\,^{2}\cdot t^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/719d993d44f966077408f116b83f48e26ef214d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:119.935ex; height:3.676ex;" alt="{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}^{2}={\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}=({\boldsymbol {{\vec {v}}_{0}}}+{\boldsymbol {\vec {a}}}\cdot t)\cdot ({\boldsymbol {{\vec {v}}_{0}}}+{\boldsymbol {\vec {a}}}\cdot t)={\boldsymbol {{\vec {v}}_{0}}}^{2}+2\cdot t\cdot ({\boldsymbol {\vec {a}}}\cdot {\boldsymbol {{\vec {v}}_{0}}})+{\boldsymbol {\vec {a}}}\,^{2}\cdot t^{2}\ \ \ \Rightarrow \ \ \ {\boldsymbol {{\vec {v}}_{(t)}}}^{2}-\,{\boldsymbol {{\vec {v}}_{0}}}^{2}=2\cdot t\cdot ({\boldsymbol {\vec {a}}}\cdot {\boldsymbol {{\vec {v}}_{0}}})+{\boldsymbol {\vec {a}}}\,^{2}\cdot t^{2}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (2{\boldsymbol {\vec {a}}})\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}=(2{\boldsymbol {\vec {a}}})\cdot ({\boldsymbol {{\vec {v}}_{0}}}\cdot t+{\frac {{\boldsymbol {\vec {a}}}\cdot t^{2}}{2}})=2\cdot t\cdot ({\boldsymbol {\vec {a}}}\cdot {\boldsymbol {{\vec {v}}_{0}}})+{\boldsymbol {\vec {a}}}\,^{2}\cdot t^{2}={\boldsymbol {{\vec {v}}_{(t)}}}^{2}-{\boldsymbol {{\vec {v}}_{0}}}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mi>t</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mo>⋅</mo> <mi>t</mi> <mo>⋅</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (2{\boldsymbol {\vec {a}}})\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}=(2{\boldsymbol {\vec {a}}})\cdot ({\boldsymbol {{\vec {v}}_{0}}}\cdot t+{\frac {{\boldsymbol {\vec {a}}}\cdot t^{2}}{2}})=2\cdot t\cdot ({\boldsymbol {\vec {a}}}\cdot {\boldsymbol {{\vec {v}}_{0}}})+{\boldsymbol {\vec {a}}}\,^{2}\cdot t^{2}={\boldsymbol {{\vec {v}}_{(t)}}}^{2}-{\boldsymbol {{\vec {v}}_{0}}}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c3772f3c86a13f19a58833d5b45ce079c488c3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:76.278ex; height:5.676ex;" alt="{\displaystyle (2{\boldsymbol {\vec {a}}})\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}=(2{\boldsymbol {\vec {a}}})\cdot ({\boldsymbol {{\vec {v}}_{0}}}\cdot t+{\frac {{\boldsymbol {\vec {a}}}\cdot t^{2}}{2}})=2\cdot t\cdot ({\boldsymbol {\vec {a}}}\cdot {\boldsymbol {{\vec {v}}_{0}}})+{\boldsymbol {\vec {a}}}\,^{2}\cdot t^{2}={\boldsymbol {{\vec {v}}_{(t)}}}^{2}-{\boldsymbol {{\vec {v}}_{0}}}^{2}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \therefore {\boldsymbol {{\vec {v}}_{(t)}}}^{2}={\boldsymbol {{\vec {v}}_{0}}}^{2}+2\cdot {\boldsymbol {\vec {a}}}\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∴</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \therefore {\boldsymbol {{\vec {v}}_{(t)}}}^{2}={\boldsymbol {{\vec {v}}_{0}}}^{2}+2\cdot {\boldsymbol {\vec {a}}}\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6dffa8b8f743b0ac479a687eaf944b1f7e9c29a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:28.25ex; height:3.676ex;" alt="{\displaystyle \therefore {\boldsymbol {{\vec {v}}_{(t)}}}^{2}={\boldsymbol {{\vec {v}}_{0}}}^{2}+2\cdot {\boldsymbol {\vec {a}}}\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}}"></span></dd></dl> <p>Ovo se može uraditi i na drugi način uzimajući <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-{\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-{\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a521c4697a3854bbcf2eb841e287244c11893a17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.902ex; height:6.343ex;" alt="{\displaystyle t={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-{\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}}"></span> iz jednačine zavisnosti trenutne brzine od vremena i uvrštavanjem istog u opštu jednačinu zavisnosti <a href="/wiki/Vektor_pomeraja" class="mw-redirect" title="Vektor pomeraja">vektora pomeraja</a> tela od vremena: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\boldsymbol {{\vec {v}}_{0}}}\cdot t+{\frac {{\boldsymbol {\vec {a}}}\cdot t^{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mi>t</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\boldsymbol {{\vec {v}}_{0}}}\cdot t+{\frac {{\boldsymbol {\vec {a}}}\cdot t^{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a474d2f2960de7d22dd2ecd3d168a1740344bf7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:22.606ex; height:5.676ex;" alt="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\boldsymbol {{\vec {v}}_{0}}}\cdot t+{\frac {{\boldsymbol {\vec {a}}}\cdot t^{2}}{2}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\boldsymbol {{\vec {v}}_{0}}}\cdot {\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-{\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}+{\frac {{\boldsymbol {\vec {a}}}\cdot \left({\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-\,{\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}\right)^{2}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>−</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\boldsymbol {{\vec {v}}_{0}}}\cdot {\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-{\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}+{\frac {{\boldsymbol {\vec {a}}}\cdot \left({\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-\,{\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}\right)^{2}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f0981de6f5a0b62cd2c9480461cae9de2323198" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:41.626ex; height:9.676ex;" alt="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\boldsymbol {{\vec {v}}_{0}}}\cdot {\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-{\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}+{\frac {{\boldsymbol {\vec {a}}}\cdot \left({\frac {{\boldsymbol {{\vec {v}}_{(t)}}}-\,{\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}\right)^{2}}{2}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{\boldsymbol {\vec {a}}}}-{\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}+{\frac {{\boldsymbol {\vec {a}}}\cdot {\frac {\left({\boldsymbol {{\vec {v}}_{(t)}}}-\,{\boldsymbol {{\vec {v}}_{0}}}\right)^{2}}{{\boldsymbol {\vec {a}}}\,^{2}}}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>−</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <msup> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{\boldsymbol {\vec {a}}}}-{\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}+{\frac {{\boldsymbol {\vec {a}}}\cdot {\frac {\left({\boldsymbol {{\vec {v}}_{(t)}}}-\,{\boldsymbol {{\vec {v}}_{0}}}\right)^{2}}{{\boldsymbol {\vec {a}}}\,^{2}}}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63421f358ce4acec97321089c1d968447affd1d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:45ex; height:9.509ex;" alt="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{\boldsymbol {\vec {a}}}}-{\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}+{\frac {{\boldsymbol {\vec {a}}}\cdot {\frac {\left({\boldsymbol {{\vec {v}}_{(t)}}}-\,{\boldsymbol {{\vec {v}}_{0}}}\right)^{2}}{{\boldsymbol {\vec {a}}}\,^{2}}}}{2}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{\boldsymbol {\vec {a}}}}-{\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}+{\frac {\frac {{\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}-\,2\cdot {\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}\,+\,{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>−</mo> <mspace width="thinmathspace" /> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mspace width="thinmathspace" /> <mo>+</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mfrac> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{\boldsymbol {\vec {a}}}}-{\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}+{\frac {\frac {{\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}-\,2\cdot {\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}\,+\,{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a88bcd1ad7efd85825bf9c1cb215b565a4b229f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:53.387ex; height:8.509ex;" alt="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{\boldsymbol {\vec {a}}}}-{\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}+{\frac {\frac {{\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}-\,2\cdot {\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}\,+\,{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{\boldsymbol {\vec {a}}}}{2}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {2\cdot {\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{2\cdot {\boldsymbol {\vec {a}}}}}-{\frac {2\cdot {\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{2\cdot {\boldsymbol {\vec {a}}}}}+{\frac {{\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{2\cdot {\boldsymbol {\vec {a}}}}}-{\frac {2\cdot {\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{2\cdot {\boldsymbol {\vec {a}}}}}+{\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{2\cdot {\boldsymbol {\vec {a}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> </mrow> <mrow> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mrow> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> </mrow> <mrow> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mrow> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> </mrow> <mrow> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {2\cdot {\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{2\cdot {\boldsymbol {\vec {a}}}}}-{\frac {2\cdot {\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{2\cdot {\boldsymbol {\vec {a}}}}}+{\frac {{\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{2\cdot {\boldsymbol {\vec {a}}}}}-{\frac {2\cdot {\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{2\cdot {\boldsymbol {\vec {a}}}}}+{\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{2\cdot {\boldsymbol {\vec {a}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e48b029b866ff17620dc91b91b46d66f54b438e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:71.517ex; height:6.343ex;" alt="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {2\cdot {\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{2\cdot {\boldsymbol {\vec {a}}}}}-{\frac {2\cdot {\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{2\cdot {\boldsymbol {\vec {a}}}}}+{\frac {{\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{(t)}}}}{2\cdot {\boldsymbol {\vec {a}}}}}-{\frac {2\cdot {\boldsymbol {{\vec {v}}_{(t)}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{2\cdot {\boldsymbol {\vec {a}}}}}+{\frac {{\boldsymbol {{\vec {v}}_{0}}}\cdot {\boldsymbol {{\vec {v}}_{0}}}}{2\cdot {\boldsymbol {\vec {a}}}}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}^{2}-{\boldsymbol {{\vec {v}}_{0}}}^{2}}{2\cdot {\boldsymbol {\vec {a}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}^{2}-{\boldsymbol {{\vec {v}}_{0}}}^{2}}{2\cdot {\boldsymbol {\vec {a}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0f881dbf21d438c656f6f7174fecca4baa2de24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:20.898ex; height:6.676ex;" alt="{\displaystyle \Delta {\boldsymbol {{\vec {r}}_{(t)}}}={\frac {{\boldsymbol {{\vec {v}}_{(t)}}}^{2}-{\boldsymbol {{\vec {v}}_{0}}}^{2}}{2\cdot {\boldsymbol {\vec {a}}}}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}^{2}-{\boldsymbol {{\vec {v}}_{0}}}^{2}=2\cdot {\boldsymbol {\vec {a}}}\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}^{2}-{\boldsymbol {{\vec {v}}_{0}}}^{2}=2\cdot {\boldsymbol {\vec {a}}}\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65b524eefe0a91b5b8bdba0a51a6ebc62a384891" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:26.054ex; height:3.676ex;" alt="{\displaystyle {\boldsymbol {{\vec {v}}_{(t)}}}^{2}-{\boldsymbol {{\vec {v}}_{0}}}^{2}=2\cdot {\boldsymbol {\vec {a}}}\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \therefore {\boldsymbol {{\vec {v}}_{(t)}}}^{2}={\boldsymbol {{\vec {v}}_{0}}}^{2}+2\cdot {\boldsymbol {\vec {a}}}\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∴</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">a</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> <mi mathvariant="bold-italic">t</mi> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \therefore {\boldsymbol {{\vec {v}}_{(t)}}}^{2}={\boldsymbol {{\vec {v}}_{0}}}^{2}+2\cdot {\boldsymbol {\vec {a}}}\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6dffa8b8f743b0ac479a687eaf944b1f7e9c29a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:28.25ex; height:3.676ex;" alt="{\displaystyle \therefore {\boldsymbol {{\vec {v}}_{(t)}}}^{2}={\boldsymbol {{\vec {v}}_{0}}}^{2}+2\cdot {\boldsymbol {\vec {a}}}\cdot \Delta {\boldsymbol {{\vec {r}}_{(t)}}}}"></span></dd></dl> <p>Gornje jednačine su validne i za <a href="/wiki/Klasi%C4%8Dna_mehanika" title="Klasična mehanika">klasičnu mehaniku</a> i za <a href="/wiki/Specijalna_relativnost" class="mw-redirect" title="Specijalna relativnost">specijalnu relativnost</a>. Ono gde se klasična mehanika i specijalna relativnost razlikuju je u tome kako različiti posmatrači opisuju jednu situaciju. Tačnije, u klasičnoj mehanici svi se posmatrači slažu u vrednosti vremena i transformacijskim pravilima vezanim za položaj što stvara situaciju u kojoj svi ne-ubrzavajući posmatrači opisuju ubrzanje tela istom vrednošću. Ovo je drugačije u specijalnoj relativnosti. Drugim rečima, moguće je izračunati samo relativnu brzinu. </p> <div class="mw-heading mw-heading2"><h2 id="Veličine_zavisne_o_brzini"><span id="Veli.C4.8Dine_zavisne_o_brzini"></span>Veličine zavisne o brzini</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=14" title="Uredi odjeljak Veličine zavisne o brzini" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=14" title="Uredi kôd odjeljka Veličine zavisne o brzini"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Kineti%C4%8Dka_energija" title="Kinetička energija">Kinetička energija</a> tela u pokretu zavisi od njegove brzine kao: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {E_{k}}}={\frac {m\cdot {\boldsymbol {v}}^{2}}{2}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold-italic">E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">k</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>m</mi> <mo>⋅</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {E_{k}}}={\frac {m\cdot {\boldsymbol {v}}^{2}}{2}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af3233cc474f52f77da8659982eb5fca553ef01d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.781ex; height:5.676ex;" alt="{\displaystyle {\boldsymbol {E_{k}}}={\frac {m\cdot {\boldsymbol {v}}^{2}}{2}},}"></span></dd></dl> <p>gde je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {E_{k}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold-italic">E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">k</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {E_{k}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b504d4e2b662a058322ab43fa88c27c6ad60c11a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.107ex; height:2.509ex;" alt="{\displaystyle {\boldsymbol {E_{k}}}}"></span> kinetička energija tela mase <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> kada ima brzinu intenziteta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2c2d3aac4213f3996d828c6aa8f4eb464a05cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.318ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {v}}}"></span>. Kinetička energija je skalarna veličina jer zavisi od kvadrata brzine (tačkasti proizvod <a href="/wiki/Vektor" title="Vektor">vektora</a>, ne vektorski, koji daje skalarnu veličinu). </p><p>Takođe vezana veličina <a href="/wiki/Impuls" title="Impuls">impuls</a> jeste vektor i definisana je kao: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {p}}=m\cdot {\boldsymbol {v}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">p</mi> </mrow> <mo>=</mo> <mi>m</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {p}}=m\cdot {\boldsymbol {v}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93252c7ac0a7b25eff9b611b0f3528b61ebd4bae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.052ex; width:10.232ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {p}}=m\cdot {\boldsymbol {v}},}"></span></dd></dl> <p>gde je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">p</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04cff366782c9fb192fc63992ef75ad59ee77695" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.052ex; width:1.449ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {p}}}"></span> impuls tela mase <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> kada ima brzinu intenziteta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b2c2d3aac4213f3996d828c6aa8f4eb464a05cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.318ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {v}}}"></span>. </p><p>U <a href="/wiki/Specijalna_relativnost" class="mw-redirect" title="Specijalna relativnost">specijalnoj relativnosti</a>, bezdimenzioni <a href="/wiki/Lorencov_faktor" class="mw-redirect" title="Lorencov faktor">Lorencov faktor</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\gamma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">γ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\gamma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1284ec96b54228a35e9c5424f848e35fe0d2251a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.434ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {\gamma }}}"></span> se javlja dosta često, i dat je izrazom: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\gamma }}={\frac {1}{\sqrt {1-{\frac {{\boldsymbol {v}}^{2}}{c^{2}}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">γ</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\gamma }}={\frac {1}{\sqrt {1-{\frac {{\boldsymbol {v}}^{2}}{c^{2}}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52fa2ca88009998d0e26b223a07732e1a2e8a24d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:14.295ex; height:8.009ex;" alt="{\displaystyle {\boldsymbol {\gamma }}={\frac {1}{\sqrt {1-{\frac {{\boldsymbol {v}}^{2}}{c^{2}}}}}}}"></span></dd></dl> <p>gde je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> <a href="/wiki/Brzina_svetlosti" class="mw-redirect" title="Brzina svetlosti">brzina svetlosti</a>. </p><p><a href="/w/index.php?title=Druga_kosmi%C4%8Dka_brzina&action=edit&redlink=1" class="new" title="Druga kosmička brzina (stranica ne postoji)">Druga kosmička brzina</a> je minimalna brzina potrebna balističkom telu da napusti <a href="/wiki/Masa" title="Masa">masivno</a> telo kao što je <a href="/wiki/Zemlja" title="Zemlja">Zemlja</a>. Predstavlja <a href="/wiki/Kineti%C4%8Dka_energija" title="Kinetička energija">kinetičku energiju</a> koja, kada se nadoda na gravitacionu <a href="/wiki/Potencijalna_energija" title="Potencijalna energija">potencijalnu energiju</a> tela (koja je uvek negativna) mora biti veća ili jednaka nuli. Generalna formula za <a href="/w/index.php?title=Druga_kosmi%C4%8Dka_brzina&action=edit&redlink=1" class="new" title="Druga kosmička brzina (stranica ne postoji)">brzinu oslobađanja</a> tela na udaljenosti <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6a5e169814762d75ef0dd3a3d0bc99b4a5a06e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {r}}}"></span> od centra planeta mase <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v_{2}}}={\sqrt {\frac {2\cdot G\cdot M}{\boldsymbol {r}}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold-italic">v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn mathvariant="bold">2</mn> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>2</mn> <mo>⋅</mo> <mi>G</mi> <mo>⋅</mo> <mi>M</mi> </mrow> <mi mathvariant="bold-italic">r</mi> </mfrac> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v_{2}}}={\sqrt {\frac {2\cdot G\cdot M}{\boldsymbol {r}}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16eefd1671e2aba6ce4e8b638f80bc368f0937f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.19ex; height:6.343ex;" alt="{\displaystyle {\boldsymbol {v_{2}}}={\sqrt {\frac {2\cdot G\cdot M}{\boldsymbol {r}}}},}"></span></dd></dl> <p>gde je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> <a href="/wiki/Gravitaciona_konstanta" class="mw-redirect" title="Gravitaciona konstanta">gravitaciona konstanta</a>. Brzina oslobađanja sa površine Zemlje je oko 11 100 m·s<sup>−1</sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Relativna_brzina">Relativna brzina</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=15" title="Uredi odjeljak Relativna brzina" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=15" title="Uredi kôd odjeljka Relativna brzina"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Relativna brzina</b> je mera brzine kretanja jednog tela u odnosu na drugo, određena u jednom <a href="/wiki/Koordinatni_sistem" class="mw-disambig" title="Koordinatni sistem">koordinatnom sistemu</a>. Relativna brzina je jedan od temeljnih principa i u klasičnoj i u modernoj fizici, jer mnogi sistemi u fizici se susreću sa relativnim kretanjima dvaju ili više tela. U <a href="/wiki/Klasi%C4%8Dna_mehanika" title="Klasična mehanika">klasičnoj mehanici</a>, relativna brzina je nezavisna od odabira inercijalnog referentnog sistema. Ovo nije slučaj i u <a href="/wiki/Specijalna_relativnost" class="mw-redirect" title="Specijalna relativnost">specijalnoj relativnosti</a> gde brzine zavise o odabiru referentnog sistema. </p><p>Ako se telo A kreće brzinom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e1b3d8e0155dc277a2aa5e3b792658ccbc46431" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.827ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}_{A}}"></span>, a telo B brzinom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6024fe933c334b27dc50e49eb813886a44d7c68" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.842ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}_{B}}"></span>, brzina tela A u odnosu na brzinu tela B (relativna brzina tela A i B) je definisana kao razlika vektora ovih dveju brzina: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}_{AB}={\boldsymbol {\vec {v}}}_{A}-{\boldsymbol {\vec {v}}}_{B}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mi>B</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}_{AB}={\boldsymbol {\vec {v}}}_{A}-{\boldsymbol {\vec {v}}}_{B}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8189bf10a6c0680360b57624dffae31d0f93679d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.33ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}_{AB}={\boldsymbol {\vec {v}}}_{A}-{\boldsymbol {\vec {v}}}_{B}.}"></span></dd></dl> <p>Slično, relativna brzina tela B koje se kreće brzinom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5532fdf5476faba7d0b1ce6847d34a6d36d00dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.798ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {v}}_{B}}"></span> u odnosu na telo A koje se kreće brzinom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2348b2c79f10713e73b5454c443d80d6fb0e48c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.783ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {v}}_{A}}"></span> je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}_{BA}={\boldsymbol {\vec {v}}}_{B}-{\boldsymbol {\vec {v}}}_{A}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>A</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}_{BA}={\boldsymbol {\vec {v}}}_{B}-{\boldsymbol {\vec {v}}}_{A}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db8268b7a5743b9fc3f1e389174117e252f08851" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.33ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}_{BA}={\boldsymbol {\vec {v}}}_{B}-{\boldsymbol {\vec {v}}}_{A}.}"></span></dd></dl> <p>Najčešće se uzima inercijalni sistem u kojem kao da jedno telo miruje, dok se drugo kreće relativnom brzinom u odnosu na njega. </p> <div class="mw-heading mw-heading3"><h3 id="Skalari">Skalari</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=16" title="Uredi odjeljak Skalari" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=16" title="Uredi kôd odjeljka Skalari"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>U <i>jednodimenzionalnom slučaju</i>, brzine se mogu razmatrati kao <a href="/wiki/Skalar_(matematika)" title="Skalar (matematika)">skalari</a>, a jednačine kretanja: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{rel}={\boldsymbol {v}}_{A}-\left(-{\boldsymbol {v}}_{B}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{rel}={\boldsymbol {v}}_{A}-\left(-{\boldsymbol {v}}_{B}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c91d787d4746f4e78504b39d66d9e929fd8125d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.719ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {v}}_{rel}={\boldsymbol {v}}_{A}-\left(-{\boldsymbol {v}}_{B}\right),}"></span>   ako se tela kreću u suprotnim smerovima, ili:</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{rel}={\boldsymbol {v}}_{A}-\left(+{\boldsymbol {v}}_{B}\right),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>−</mo> <mrow> <mo>(</mo> <mrow> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{rel}={\boldsymbol {v}}_{A}-\left(+{\boldsymbol {v}}_{B}\right),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/569de7e29276f5d439f5022ddeb951df756348fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.719ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {v}}_{rel}={\boldsymbol {v}}_{A}-\left(+{\boldsymbol {v}}_{B}\right),}"></span>   ako se tela kreću u istom smeru.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Polarne_koordinate">Polarne koordinate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=17" title="Uredi odjeljak Polarne koordinate" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=17" title="Uredi kôd odjeljka Polarne koordinate"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kod <a href="/wiki/Polarni_koordinatni_sistem" class="mw-redirect" title="Polarni koordinatni sistem">polarnih koordinata</a>, dvodimenzionalna brzina se opisuje kao <b>radijalna brzina</b>, definisana kao komponenta brzine <i>od ishodišta</i> ili <i>prema ishodištu</i> (takođe poznata i kao <a href="/wiki/Engleski_jezik" title="Engleski jezik">engl.</a> <i><span lang="en">velocity made good</span></i>) ili <a href="/wiki/Ugaona_brzina" class="mw-redirect" title="Ugaona brzina">ugaona brzina</a> koja predstavlja prvi izvod <a href="/w/index.php?title=Vektor_ugaonog_polo%C5%BEaja&action=edit&redlink=1" class="new" title="Vektor ugaonog položaja (stranica ne postoji)">vektora ugaonog položaja</a> tela po vremenu (sa pozitivnim veličinama za smer suprotan smeru kazaljki na sati, i negativnim za smer jednak smeru kazaljki na sati, u sistemu <a href="/w/index.php?title=Desni_zavrtanj&action=edit&redlink=1" class="new" title="Desni zavrtanj (stranica ne postoji)">desnog zavrtnja</a>). </p><p>Radijalna i ugaona brzina se mogu izvesti iz vektora brzine i <a href="/wiki/Vektor_pomeraja" class="mw-redirect" title="Vektor pomeraja">vektora pomeraja</a> u <a href="/wiki/Dekartov_koordinatni_sistem" class="mw-redirect" title="Dekartov koordinatni sistem">DKS</a>-u, rastavljanjem vektora brzine na tangencijalnu i normalnu komponentu. <b>Normalna brzina</b> je komponenta brzine duž <a href="/wiki/Kru%C5%BEnica" title="Kružnica">kružnice</a> usmerena ka njenom centru. </p><p>Ukupna brzina tela koje se kreće po kružnici je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {v}}}={\boldsymbol {\vec {v}}}_{N}+{\boldsymbol {\vec {v}}}_{T},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>=</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {v}}}={\boldsymbol {\vec {v}}}_{N}+{\boldsymbol {\vec {v}}}_{T},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91ff2b07dca58a673451d87d2462fe0210ec06d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.754ex; height:2.676ex;" alt="{\displaystyle {\boldsymbol {\vec {v}}}={\boldsymbol {\vec {v}}}_{N}+{\boldsymbol {\vec {v}}}_{T},}"></span></dd></dl> <p>gde je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{N}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{N}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc0192c35118a16f3e9c02855c37c806333ab037" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.01ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {v}}_{N}}"></span> normalna brzina, a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43c40e468c9cb22f80dec9b4d32e7be3e30596cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.707ex; height:2.009ex;" alt="{\displaystyle {\boldsymbol {v}}_{T}}"></span> tangencijalna brzina. </p><p>Intenzitet tangencijalne brzine je tačkasti proizvod vektora brzine i jediničnog vektora u smeru <a href="/wiki/Pomeraj" title="Pomeraj">pomeraja</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{T}={\boldsymbol {\vec {v}}}\cdot {\frac {\boldsymbol {\vec {r}}}{|{\boldsymbol {\vec {r}}}\,|}}={\boldsymbol {\vec {v}}}\cdot {\boldsymbol {\hat {r}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{T}={\boldsymbol {\vec {v}}}\cdot {\frac {\boldsymbol {\vec {r}}}{|{\boldsymbol {\vec {r}}}\,|}}={\boldsymbol {\vec {v}}}\cdot {\boldsymbol {\hat {r}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06b0c019ffeb5cfe61a795280a796dd00bceed20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:21.044ex; height:6.343ex;" alt="{\displaystyle {\boldsymbol {v}}_{T}={\boldsymbol {\vec {v}}}\cdot {\frac {\boldsymbol {\vec {r}}}{|{\boldsymbol {\vec {r}}}\,|}}={\boldsymbol {\vec {v}}}\cdot {\boldsymbol {\hat {r}}},}"></span></dd></dl> <p>gde je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\vec {r}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\vec {r}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac8a6c987cd2becc815131033ed1f3872bd7dd74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.407ex; height:2.343ex;" alt="{\displaystyle {\boldsymbol {\vec {r}}}}"></span> <a href="/wiki/Vektor_polo%C5%BEaja" class="mw-redirect" title="Vektor položaja">vektor položaja</a>. </p><p>Intenzitet normalne brzine je vektorski proizvod vektora brzine i jediničnog vektora u smeru <a href="/wiki/Pomeraj" title="Pomeraj">pomeraja</a> , ili — proizvod intenziteta ugaone brzine <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\omega }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\omega }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cb8af7a2f64af348e559652b6b1f0d2415ba444" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.669ex; height:1.676ex;" alt="{\displaystyle {\boldsymbol {\omega }}}"></span> i intenziteta vektora položaja: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {v}}_{N}={\boldsymbol {\vec {v}}}\times {\frac {\boldsymbol {\vec {r}}}{|{\boldsymbol {\vec {r}}}\,|}}={\boldsymbol {\vec {v}}}\times {\boldsymbol {\hat {r}}}={\frac {|{\boldsymbol {\vec {v}}}\times {\boldsymbol {\vec {r}}}\,|}{\boldsymbol {\vec {r}}}}={\boldsymbol {\omega }}\cdot |{\boldsymbol {\vec {r}}}\,|={\boldsymbol {\omega }}\cdot {\boldsymbol {r}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">^</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">v</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {v}}_{N}={\boldsymbol {\vec {v}}}\times {\frac {\boldsymbol {\vec {r}}}{|{\boldsymbol {\vec {r}}}\,|}}={\boldsymbol {\vec {v}}}\times {\boldsymbol {\hat {r}}}={\frac {|{\boldsymbol {\vec {v}}}\times {\boldsymbol {\vec {r}}}\,|}{\boldsymbol {\vec {r}}}}={\boldsymbol {\omega }}\cdot |{\boldsymbol {\vec {r}}}\,|={\boldsymbol {\omega }}\cdot {\boldsymbol {r}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5997ab6d3dd95f614f8bd54122a1ff5f4b11485" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:52.105ex; height:6.509ex;" alt="{\displaystyle {\boldsymbol {v}}_{N}={\boldsymbol {\vec {v}}}\times {\frac {\boldsymbol {\vec {r}}}{|{\boldsymbol {\vec {r}}}\,|}}={\boldsymbol {\vec {v}}}\times {\boldsymbol {\hat {r}}}={\frac {|{\boldsymbol {\vec {v}}}\times {\boldsymbol {\vec {r}}}\,|}{\boldsymbol {\vec {r}}}}={\boldsymbol {\omega }}\cdot |{\boldsymbol {\vec {r}}}\,|={\boldsymbol {\omega }}\cdot {\boldsymbol {r}},}"></span></dd></dl> <p>tako da je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {\omega }}={\frac {|{\boldsymbol {v}}\times {\boldsymbol {\vec {r}}}\,|}{|{\boldsymbol {\vec {r}}}\,|^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {\omega }}={\frac {|{\boldsymbol {v}}\times {\boldsymbol {\vec {r}}}\,|}{|{\boldsymbol {\vec {r}}}\,|^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d554394ec0874da474f7c079e1c0b88885cf193" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:13.497ex; height:6.843ex;" alt="{\displaystyle {\boldsymbol {\omega }}={\frac {|{\boldsymbol {v}}\times {\boldsymbol {\vec {r}}}\,|}{|{\boldsymbol {\vec {r}}}\,|^{2}}}.}"></span></dd></dl> <p><a href="/wiki/Ugaoni_moment" title="Ugaoni moment">Ugaoni moment</a> u <a href="/wiki/Skalar_(matematika)" title="Skalar (matematika)">skalarnom</a> obliku je proizvod mase, <a href="/wiki/Polo%C5%BEaj" class="mw-redirect" title="Položaj">položaja</a> (udaljenosti od ishodišta) i normalne brzine, ili ekvivalentno — proizvod mase, kvadrata <a href="/wiki/Polo%C5%BEaj" class="mw-redirect" title="Položaj">položaja</a> i intenziteta ugaone brzine: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {L}}=m\cdot {\boldsymbol {r}}\cdot {\boldsymbol {v}}_{T}=m\cdot {\boldsymbol {r}}^{2}\cdot {\boldsymbol {\omega }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">L</mi> </mrow> <mo>=</mo> <mi>m</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>⋅</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">v</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mo>⋅</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {L}}=m\cdot {\boldsymbol {r}}\cdot {\boldsymbol {v}}_{T}=m\cdot {\boldsymbol {r}}^{2}\cdot {\boldsymbol {\omega }},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bff7af8e728e032cff06993ac3d66567532cb9ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:27.288ex; height:3.009ex;" alt="{\displaystyle {\boldsymbol {L}}=m\cdot {\boldsymbol {r}}\cdot {\boldsymbol {v}}_{T}=m\cdot {\boldsymbol {r}}^{2}\cdot {\boldsymbol {\omega }},}"></span></dd></dl> <p>gde je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> masa, a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {r}}=|{\boldsymbol {\vec {r}}}\,|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="bold-italic">r</mi> <mo mathvariant="bold" stretchy="false">→</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {r}}=|{\boldsymbol {\vec {r}}}\,|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9e1a92bb7ceecfcb1ba5cb81fe35728b3cfe84c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.416ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {r}}=|{\boldsymbol {\vec {r}}}\,|}"></span> intenzitet vektora položaja. </p><p>Izraz <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ m{\boldsymbol {r}}^{2}\ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>m</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ m{\boldsymbol {r}}^{2}\ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29f902112c1b2aa2833293a505b69d4210ef39fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.486ex; height:2.676ex;" alt="{\displaystyle \ m{\boldsymbol {r}}^{2}\ }"></span> je poznat pod imenom <a href="/wiki/Moment_inercije" title="Moment inercije">moment inercije</a>. </p><p>Ako su sile u radijalnom smeru samo u obrnutoj kvadratnoj zavisnosti, kao što je to slučaj sa gravtitacionom orbitom, ugaoni moment je konstantan, a normalna brzina obrnuto proporcionalna udaljenosti, ugaona brzina obrnuto proprcionalna kvadratu udaljenosti, a izvod po kojem je površina vađena je konstantan. Ove relacije su poznate kao <a href="/wiki/Keplerovi_zakoni_planetarnog_kretanja" title="Keplerovi zakoni planetarnog kretanja">Keplerovi zakoni planetarnog kretanja</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Povezano">Povezano</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=18" title="Uredi odjeljak Povezano" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=18" title="Uredi kôd odjeljka Povezano"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Gibanje" class="mw-redirect" title="Gibanje">Gibanje</a></li> <li><a href="/wiki/Putanja" title="Putanja">Putanja</a></li> <li><a href="/wiki/Ubrzanje" title="Ubrzanje">Ubrzanje</a></li> <li><a href="/wiki/Trzaj" title="Trzaj">Trzaj</a></li> <li><a href="/w/index.php?title=Prva_kosmi%C4%8Dka_brzina&action=edit&redlink=1" class="new" title="Prva kosmička brzina (stranica ne postoji)">Prva kosmička brzina</a></li> <li><a href="/w/index.php?title=Druga_kosmi%C4%8Dka_brzina&action=edit&redlink=1" class="new" title="Druga kosmička brzina (stranica ne postoji)">Druga kosmička brzina</a></li> <li><a href="/w/index.php?title=Tre%C4%87a_kosmi%C4%8Dka_brzina&action=edit&redlink=1" class="new" title="Treća kosmička brzina (stranica ne postoji)">Treća kosmička brzina</a></li> <li><a href="/w/index.php?title=%C4%8Cetvrta_kosmi%C4%8Dka_brzina&action=edit&redlink=1" class="new" title="Četvrta kosmička brzina (stranica ne postoji)">Četvrta kosmička brzina</a></li> <li><a href="/wiki/Polo%C5%BEaj" class="mw-redirect" title="Položaj">Položaj</a></li> <li><a href="/wiki/Vektor_polo%C5%BEaja" class="mw-redirect" title="Vektor položaja">Vektor položaja</a></li> <li><a href="/wiki/Pomeraj" title="Pomeraj">Pomeraj</a></li> <li><a href="/wiki/Vektor_pomeraja" class="mw-redirect" title="Vektor pomeraja">Vektor pomeraja</a></li> <li><a href="/wiki/Ugaona_brzina" class="mw-redirect" title="Ugaona brzina">Ugaona brzina</a></li> <li><a href="/wiki/Brzina_svetlosti" class="mw-redirect" title="Brzina svetlosti">Brzina svetlosti</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Literatura">Literatura</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=19" title="Uredi odjeljak Literatura" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=19" title="Uredi kôd odjeljka Literatura"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r41379810">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}</style><div class="refbegin" style=""> <ul><li>Robert Resnick and Jearl Walker, <i>Fundamentals of Physics</i>, Wiley; 7 Sub edition (June 16, 2004). <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Posebno:Tra%C5%BEi_ISBN/0-471-23231-9" title="Posebno:Traži ISBN/0-471-23231-9">0-471-23231-9</a>.</li> <li><span class="citation book" id="CITEREFGribbinGribbinGribbin1998">Gribbin, J.R.; Gribbin, M.; Gribbin, J. (1998). <a rel="nofollow" class="external text" href="http://books.google.com/books?id=WzwbAQAAIAAJ"><i>Q is for Quantum: An Encyclopedia of Particle Physics</i></a>. Free Press. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Posebno:Tra%C5%BEi_ISBN/978-0-684-85578-3" title="Posebno:Traži ISBN/978-0-684-85578-3">978-0-684-85578-3</a>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Q+is+for+Quantum%3A+An+Encyclopedia+of+Particle+Physics&rft.aulast=Gribbin&rft.aufirst=J.R.&rft.au=Gribbin%2C%26%2332%3BJ.R.&rft.au=Gribbin%2C%26%2332%3BM.&rft.au=Gribbin%2C%26%2332%3BJ.&rft.date=1998&rft.pub=Free+Press&rft.isbn=978-0-684-85578-3&rft_id=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DWzwbAQAAIAAJ&rfr_id=info:sid/en.wikipedia.org:Brzina"><span style="display: none;"> </span></span></li> <li><span class="citation book" id="CITEREFGribbinGribbinGribbin1998">Gribbin, J.R.; Gribbin, M.; Gribbin, J. (1998). <a rel="nofollow" class="external text" href="http://books.google.com/books?id=WzwbAQAAIAAJ"><i>Q is for Quantum: An Encyclopedia of Particle Physics</i></a>. Free Press. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Posebno:Tra%C5%BEi_ISBN/978-0-684-85578-3" title="Posebno:Traži ISBN/978-0-684-85578-3">978-0-684-85578-3</a>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Q+is+for+Quantum%3A+An+Encyclopedia+of+Particle+Physics&rft.aulast=Gribbin&rft.aufirst=J.R.&rft.au=Gribbin%2C%26%2332%3BJ.R.&rft.au=Gribbin%2C%26%2332%3BM.&rft.au=Gribbin%2C%26%2332%3BJ.&rft.date=1998&rft.pub=Free+Press&rft.isbn=978-0-684-85578-3&rft_id=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DWzwbAQAAIAAJ&rfr_id=info:sid/en.wikipedia.org:Brzina"><span style="display: none;"> </span></span></li> <li><span class="citation book" id="CITEREFHolzner2006">Holzner, S. (2006). <a rel="nofollow" class="external text" href="https://www.amazon.com/gp/reader/0764554336"><i>Physics for Dummies</i></a>. John Wiley & Sons. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Posebno:Tra%C5%BEi_ISBN/0-470-61841-8" title="Posebno:Traži ISBN/0-470-61841-8">0-470-61841-8</a>. »Physics is the study of your world and the world and universe around you.«</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+Dummies&rft.aulast=Holzner&rft.aufirst=S.&rft.au=Holzner%2C%26%2332%3BS.&rft.date=2006&rft.pub=John+Wiley+%26+Sons&rft.isbn=0-470-61841-8&rft_id=http%3A%2F%2Fwww.amazon.com%2Fgp%2Freader%2F0764554336&rfr_id=info:sid/en.wikipedia.org:Brzina"><span style="display: none;"> </span></span></li> <li><span class="citation Journal" id="CITEREFLeggett1999">Leggett, A.J. (1999). „Superfluidity”. <i>Reviews of Modern Physics</i> <b>71</b> (2): S318–S323. <a href="/wiki/Bibcode" title="Bibcode">Bibcode</a> <a rel="nofollow" class="external text" href="http://adsabs.harvard.edu/abs/1999RvMPS..71..318L">1999RvMPS..71..318L</a>. <a href="/wiki/Digitalni_identifikator_objekta" title="Digitalni identifikator objekta">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1103%2FRevModPhys.71.S318">10.1103/RevModPhys.71.S318</a>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Superfluidity&rft.jtitle=Reviews+of+Modern+Physics&rft.aulast=Leggett&rft.aufirst=A.J.&rft.au=Leggett%2C%26%2332%3BA.J.&rft.date=1999&rft.volume=71&rft.issue=2&rft.pages=S318%E2%80%93S323&rft_id=info:bibcode/1999RvMPS..71..318L&rft_id=info:doi/10.1103%2FRevModPhys.71.S318&rfr_id=info:sid/en.wikipedia.org:Brzina"><span style="display: none;"> </span></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Vanjske_veze">Vanjske veze</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brzina&veaction=edit&section=20" title="Uredi odjeljak Vanjske veze" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Brzina&action=edit&section=20" title="Uredi kôd odjeljka Vanjske veze"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="infobox sisterproject" style="width: 300px"> <div style="float: left;"><figure class="mw-halign-none" typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/Category:Velocity" title="commons:Category:Velocity"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a><figcaption></figcaption></figure></div> <div style="margin-left: 20px;"><i><b><a href="https://commons.wikimedia.org/wiki/Category:Velocity" class="extiw" title="commons:Category:Velocity">Brzina</a></b></i> na <a href="https://commons.wikimedia.org/wiki/Glavna_stranica_-_%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B0" class="extiw" title="commons:Glavna stranica - Главна страница">Wikimedijinoj ostavi</a> </div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.physicsclassroom.com/Class/1DKin/U1L1d.html">Physicsclassroom.com</a>, Speed and Velocity</li> <li><a rel="nofollow" class="external text" href="http://www.scs.cmu.edu/~rapidproto/mechanisms/chpt1.html">Introduction to Mechanisms</a> (Carnegie Mellon University)</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="" lang="sh-Latn" dir="ltr">Izvor: <a dir="ltr" href="https://sh.wikipedia.org/w/index.php?title=Brzina&oldid=42041724">https://sh.wikipedia.org/w/index.php?title=Brzina&oldid=42041724</a></div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Posebno:Kategorije" title="Posebno:Kategorije">Kategorija</a>: <ul><li><a href="/wiki/Kategorija:Kretanje" title="Kategorija:Kretanje">Kretanje</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" lang="sh-Latn" dir="ltr"> <ul id="footer-info"> <li id="footer-info-lastmod"> Ova stranica je posljednji put izmijenjena 27. jula 2024. u 02:14.</li> <li id="footer-info-copyright">Tekst je dostupan pod licencom <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-ShareAlike</a>; mogu se primijeniti i dodatni uslovi. 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