Velocity | Speed, Acceleration, Motion

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class="drawer d-flex flex-column open"> <div class="left-rail-section-content"> <div class="topic-left-rail-header text-truncate bg-gray-50 position-relative text-right d-flex align-items-center"> <div class="tlr-title px-20 py-15 text-left"> <em class="material-icons text-gray-400 d-lg-none" data-icon="toc"></em> <a class="font-serif font-weight-bold text-black link-blue" href="https://www.britannica.com/science/velocity">velocity</a> </div> <button aria-label="Close" class="js-sections-close-button btn-link btn-sm btn d-lg-none position-absolute top-0 p-10 right-0" > <em class="material-icons font-26" data-icon="close"></em> </button> </div> <div class="section-content pl-10 pr-20 pl-sm-50 pr-sm-60 pl-lg-5 pr-lg-10 pt-10 pt-lg-0 bg-gray-50 clear-catfish-ad"> <div class="toc mb-20"> <div class="font-serif font-14 font-weight-bold mx-15 mb-15 mt-20"> Table of Contents </div> <span class="toc-extra-link selected link-gray-900 mt-15"> Introduction </span> <a class="toc-extra-link link-gray-900" href="https://www.britannica.com/science/velocity/additional-info">References & Edit History</a> <a class="toc-extra-link link-gray-900" href="/facts/velocity">Related Topics</a> </div> <div class="tlr-media-slider pb-10 mb-30"> <a class="section-header link-gray-900 font-serif font-14 font-weight-bold mb-10 mx-10" href="https://www.britannica.com/science/velocity/images-videos">Images</a> <div class="slider js-slider position-relative d-inline-flex align-items-center mw-100 "> <div class="slider-container js-slider-container overflow-hidden d-flex overflow-hidden text-nowrap ml-15"> <a href="https://cdn.britannica.com/41/2941-004-E9AB5656/triangle-course-aicraft-vector-compass-heading-aircraft.jpg" data-href="/media/1/624901/2589" class="media-overlay-link d-inline-block mr-5"> <img loading="lazy" src="https://cdn.britannica.com/41/2941-004-E9AB5656/triangle-course-aicraft-vector-compass-heading-aircraft.jpg" alt="determining the course of an aircraft" height="50" /> 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They write new content and verify and edit content received from contributors.</div> </a> <div data-popper-arrow></div> </div> <span class="btn btn-link editor-link p-0 qa-byline-link gtm-byline font-12 byline-contributor text-decoration-underline"> The Editors of Encyclopaedia Britannica</span></div> <div class="last-updated font-12 font-serif"> <span class="text-gray-700"> Last Updated: <time datetime="2025-01-24T00:00:00CST" >Jan 24, 2025</time> •</span> <a class="byline-edit-history" href="https://www.britannica.com/science/velocity/additional-info#history" rel="nofollow">Article History</a> </div></div> </div> <button class="d-flex d-lg-none btn btn-outline-blue border rounded-sm shadow-sm mobile-toc-button gtm-mobile-toc-inline-button d-none d-sm-block js-sections-inline-button module-spacing btn d-lg-none"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="toc"></em> Table of Contents </button> <div class="d-flex d-sm-none flex-row"> <button class="d-flex d-lg-none btn btn-outline-blue border rounded-sm shadow-sm mobile-toc-button gtm-mobile-toc-inline-button js-sections-inline-button module-spacing"> <em class="material-icons mr-5 ml-n10 my-n5 md-icon" data-icon="toc"></em> Table of Contents </button> <button class="ai-ask-button btn btn-sm border-2 btn-outline-red-400 border-red-400 module-spacing js-inline-ai-ask-button p-10 ml-5"> Ask the Chatbot </button> </div> <div class="js-qf-module qf-module px-40 px-sm-20 py-15 mx-auto module-spacing font-14 bg-gray-50 rounded"> <div class="facts-list mt-10"> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>Key People: </dt> <dd><a href="/biography/Antoine-de-Chezy" topicid="109968">Antoine de Chézy</a></dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show more)</em> </button> </div> </div> <div class=""> <div class="js-fact mb-10 line-clamp clamp-3"> <dl> <dt>Related Topics: </dt> <dd><a href="/science/wave-velocity" topicid="637913">wave velocity</a></dd> <dd><a href="/science/angular-velocity" topicid="25354">angular velocity</a></dd> <dd><a href="/science/terminal-velocity" topicid="588001">terminal velocity</a></dd> <dd><a href="/science/orbital-velocity" topicid="431205">orbital velocity</a></dd> <dd><a href="/science/acceleration" topicid="2810">acceleration</a></dd> </dl> <button class="js-more-btn d-none btn btn-unstyled font-12 bg-gray-50" aria-label="Toggle more/less fact data"> <em class="js-content link-blue">(Show more)</em> </button> </div> <div class="text-center"> <a class="btn btn-sm btn-link p-0" href="/facts/velocity"> See all related content </a> </div> </div> </div> </div><span class="marker before-article"></span><section data-level="1" id="ref1"><span class="marker PREMOD1 mod-inline"></span><p class="topic-paragraph"><strong><span id="ref268530"></span>velocity</strong>, quantity that <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="designates" href="https://www.britannica.com/dictionary/designates" data-type="EB">designates</a> how fast and in what direction a point is moving. A point always moves in a direction that is <a href="https://www.britannica.com/science/tangent-of-a-curve" class="md-crosslink autoxref " data-show-preview="true">tangent</a> to its path; for a circular path, for example, its direction at any instant is perpendicular to a line from the point to the centre of the <a href="https://www.britannica.com/science/circle-mathematics" class="md-crosslink autoxref " data-show-preview="true">circle</a> (a radius). The magnitude of the velocity (i.e., the <span id="ref1264866"></span><a href="https://www.britannica.com/science/speed-mechanics" class="md-crosslink ">speed</a>) is the time rate at which the point is moving along its path.</p><span class="marker MOD1 mod-inline"></span><span class="marker PREMOD2 mod-inline"></span><p class="topic-paragraph">If a point moves a certain distance along its path in a given time interval, its average speed during the interval is equal to the distance moved divided by the time taken. A train that travels 100 km in 2 hours, for example, has an average speed of 50 km per hour.</p><span class="marker MOD2 mod-inline"></span><span class="marker PREMOD3 mod-inline"></span><p class="topic-paragraph">During the two-hour interval, the speed of the train in the previous example may have varied considerably around the average. The speed of a point at any instant may be approximated by finding the average speed for a short time interval including the instant in question. The <span id="ref268531"></span><a href="https://www.britannica.com/science/differential-calculus" class="md-crosslink " data-show-preview="true">differential calculus</a>, which was invented by <a href="https://www.britannica.com/biography/Isaac-Newton" class="md-crosslink autoxref " data-show-preview="true">Isaac Newton</a> for this specific purpose, provides means for determining exact <a class="md-dictionary-link md-dictionary-tt-off eb" data-term="values" href="https://www.britannica.com/dictionary/values" data-type="EB">values</a> of the instantaneous velocity.</p><a class="link-module shadow-sm d-block qa-quiz-module" href="/quiz/fun-facts-of-measurement-math" data-link-module-iframe-link=""> <img loading="lazy" src="https://cdn.britannica.com/68/166068-131-03976F7B/barometer-Barometer-Technology-measurement-readout-pressure-mathematics.jpg" alt="barometer. Antique Barometer with readout. Technology measurement, mathematics, measure atmospheric pressure" class="rounded-sm mr-15" width="70" /> <div class="line-clamp clamp-5"> <div class="module-title bg-green">Britannica Quiz</div> <div class="font-weight-semi-bold mt-5">Fun Facts of Measurement & Math</div> </div> </a><div class="one-good-fact-module"> </div><span class="marker MOD3 mod-inline"></span><span class="marker PREMOD4 mod-inline"></span><p class="topic-paragraph">Because it has direction as well as magnitude, velocity is known as a <span id="ref893557"></span><a href="https://www.britannica.com/science/vector-mathematics" class="md-crosslink " data-show-preview="true">vector</a> quantity and cannot be specified completely by a number, as can be done with time or length, which are scalar quantities. Like all vectors, velocity is represented graphically by a directed line segment (arrow) the length of which is proportional to its magnitude.</p><span class="marker MOD4 mod-inline"></span></section> <span class="md-signature font-12">This article was most recently revised and updated by <a href="/editor/William-L-Hosch/6481">William L. 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