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Acceleration - Wikipedia
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.hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style> <div role="note" class="hatnote navigation-not-searchable"> This article is about acceleration in physics. For other uses, see <a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration_(disambiguation)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-disambig" title="Acceleration (disambiguation)">Acceleration (disambiguation)</a>. </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"> <div role="note" class="hatnote navigation-not-searchable"> "Accelerate" redirects here. For other uses, see <a href="https://en-m-wikipedia-org.translate.goog/wiki/Accelerate_(disambiguation)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-disambig" title="Accelerate (disambiguation)">Accelerate (disambiguation)</a>. </div> <p class="mw-empty-elt"></p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style> <p>In <a href="https://en-m-wikipedia-org.translate.goog/wiki/Mechanics?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Mechanics">mechanics</a>, <b>acceleration</b> is the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Rate_(mathematics)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Rate (mathematics)">rate</a> of change of the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Velocity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Velocity">velocity</a> of an object with respect to time. Acceleration is one of several components of <a href="https://en-m-wikipedia-org.translate.goog/wiki/Kinematics?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Kinematics">kinematics</a>, the study of <a href="https://en-m-wikipedia-org.translate.goog/wiki/Motion?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Motion">motion</a>. Accelerations are <a href="https://en-m-wikipedia-org.translate.goog/wiki/Euclidean_vector?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Euclidean vector">vector</a> quantities (in that they have <a href="https://en-m-wikipedia-org.translate.goog/wiki/Magnitude_(mathematics)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Magnitude (mathematics)">magnitude</a> and <a href="https://en-m-wikipedia-org.translate.goog/wiki/Direction_(geometry)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Direction (geometry)">direction</a>).<sup id="cite_ref-1" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The orientation of an object's acceleration is given by the orientation of the <i>net</i> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Force">force</a> acting on that object. The magnitude of an object's acceleration, as described by <a href="https://en-m-wikipedia-org.translate.goog/wiki/Newton%27s_Second_Law?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Newton's Second Law">Newton's Second Law</a>,<sup id="cite_ref-3" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> is the combined effect of two causes:</p> <ul> <li>the net balance of all external <a href="https://en-m-wikipedia-org.translate.goog/wiki/Force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Force">forces</a> acting onto that object — magnitude is <a href="https://en-m-wikipedia-org.translate.goog/wiki/Direct_proportionality?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Direct proportionality">directly proportional</a> to this net resulting force;</li> <li>that object's <a href="https://en-m-wikipedia-org.translate.goog/wiki/Mass?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Mass">mass</a>, depending on the materials out of which it is made — magnitude is <a href="https://en-m-wikipedia-org.translate.goog/wiki/Inverse_proportionality?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Inverse proportionality">inversely proportional</a> to the object's mass.</li> </ul> <table class="infobox"> <tbody> <tr> <th colspan="2" class="infobox-above">Acceleration</th> </tr> <tr> <td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="https://en-m-wikipedia-org.translate.goog/wiki/File:Gravity_gravita_grave.gif?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Gravity_gravita_grave.gif/220px-Gravity_gravita_grave.gif" decoding="async" width="220" height="304" class="mw-file-element" srcset="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://upload.wikimedia.org/wikipedia/commons/7/7d/Gravity_gravita_grave.gif 1.5x" data-file-width="289" data-file-height="400"></a></span> <div class="infobox-caption"> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"> In vacuum (no <a href="https://en-m-wikipedia-org.translate.goog/wiki/Drag_(physics)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Drag (physics)">air resistance</a>), objects attracted by Earth gain speed at a steady rate. </div> </div></td> </tr> <tr> <th scope="row" class="infobox-label"> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"> Common symbols </div></th> <td class="infobox-data"><b>a</b></td> </tr> <tr> <th scope="row" class="infobox-label"><a href="https://en-m-wikipedia-org.translate.goog/wiki/SI_unit?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="SI unit">SI unit</a></th> <td class="infobox-data"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Metre_per_second_squared?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Metre per second squared">m/s<sup>2</sup>, m·s<sup>−2</sup>, m s<sup>−2</sup></a></td> </tr> <tr> <th scope="row" class="infobox-label"> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"> Derivations from<br> other quantities </div></th> <td class="infobox-data"><span class="mwe-math-element" data-qid="Q11376"><a href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Special:MathWikibase&qid=Q11376&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" style="color:inherit;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> x </mi> </mrow> </mrow> <mrow> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}} </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1760b1620e8d07692ecfb879abb37fad5a34f238" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.479ex; height:6.009ex;" alt="{\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}}"></a></span></td> </tr> <tr> <th scope="row" class="infobox-label"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Dimensional_analysis?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Formulation" title="Dimensional analysis">Dimension</a></th> <td class="infobox-data"><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 {\mathsf {L}}{\mathsf {T}}^{-2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif"> L </mi> </mrow> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif"> T </mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo> −<!-- − --> </mo> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\mathsf {L}}{\mathsf {T}}^{-2}} </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2639355e0e107e11e7d06c0f772f155c24a0ed1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.176ex; height:2.676ex;" alt="{\displaystyle {\mathsf {L}}{\mathsf {T}}^{-2}}"></span></td> </tr> </tbody> </table> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist 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a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <figure class="mw-default-size" typeof="mw:File/Thumb"> <a href="https://en-m-wikipedia-org.translate.goog/wiki/File:DonPrudhommeFire1991KennyBernstein.jpg?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/DonPrudhommeFire1991KennyBernstein.jpg/310px-DonPrudhommeFire1991KennyBernstein.jpg" decoding="async" width="310" height="167" class="mw-file-element" srcset="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://upload.wikimedia.org/wikipedia/commons/thumb/6/6a/DonPrudhommeFire1991KennyBernstein.jpg/465px-DonPrudhommeFire1991KennyBernstein.jpg 1.5x,https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://upload.wikimedia.org/wikipedia/commons/6/6a/DonPrudhommeFire1991KennyBernstein.jpg 2x" data-file-width="600" data-file-height="324"></a> <figcaption> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Drag_racing?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Drag racing">Drag racing</a> is a sport in which specially-built vehicles compete to be the fastest to accelerate from a standing start. </figcaption> </figure> <p>The <a href="https://en-m-wikipedia-org.translate.goog/wiki/International_System_of_Units?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="International System of Units">SI</a> unit for acceleration is <a href="https://en-m-wikipedia-org.translate.goog/wiki/Metre_per_second_squared?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Metre per second squared">metre per second squared</a> (<span class="nowrap">m⋅s<sup>−2</sup></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 \mathrm {\tfrac {m}{s^{2}}} }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi mathvariant="normal"> m </mi> <msup> <mi mathvariant="normal"> s </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathrm {\tfrac {m}{s^{2}}} } </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98dfac31f9b284074d7828a73a97246a48a9f41d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:2.316ex; height:3.509ex;" alt="{\displaystyle \mathrm {\tfrac {m}{s^{2}}} }"></span>).</p> <p>For example, when a <a href="https://en-m-wikipedia-org.translate.goog/wiki/Vehicle?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Vehicle">vehicle</a> starts from a <a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://en.wiktionary.org/wiki/standstill" class="extiw" title="wikt:standstill">standstill</a> (zero velocity, in an <a href="https://en-m-wikipedia-org.translate.goog/wiki/Inertial_frame_of_reference?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Inertial frame of reference">inertial frame of reference</a>) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the vehicle turns, an acceleration occurs toward the new direction and changes its motion vector. The acceleration of the vehicle in its current direction of motion is called a linear (or tangential during <a href="https://en-m-wikipedia-org.translate.goog/wiki/Circular_motion?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Circular motion">circular motions</a>) acceleration, the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Reaction_(physics)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Reaction (physics)">reaction</a> to which the passengers on board experience as a force pushing them back into their seats. When changing direction, the effecting acceleration is called radial (or centripetal during circular motions) acceleration, the reaction to which the passengers experience as a <a href="https://en-m-wikipedia-org.translate.goog/wiki/Centrifugal_force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Centrifugal force">centrifugal force</a>. If the speed of the vehicle decreases, this is an acceleration in the opposite direction of the velocity vector (mathematically a <a href="https://en-m-wikipedia-org.translate.goog/wiki/Negative_number?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Negative number">negative</a>, if the movement is unidimensional and the velocity is positive), sometimes called <b>deceleration</b><sup id="cite_ref-4" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> or <b>retardation</b>, and passengers experience the reaction to deceleration as an <a href="https://en-m-wikipedia-org.translate.goog/wiki/Inertia?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Inertia">inertial</a> force pushing them forward. Such negative accelerations are often achieved by <a href="https://en-m-wikipedia-org.translate.goog/wiki/Retrorocket?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Retrorocket">retrorocket</a> burning in <a href="https://en-m-wikipedia-org.translate.goog/wiki/Spacecraft?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Spacecraft">spacecraft</a>.<sup id="cite_ref-6" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Both acceleration and deceleration are treated the same, as they are both changes in velocity. Each of these accelerations (tangential, radial, deceleration) is felt by passengers until their relative (differential) velocity are neutralized in <a href="https://en-m-wikipedia-org.translate.goog/wiki/Frame_of_reference?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Frame of reference">reference</a> to the acceleration due to change in speed.</p> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"> <input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"> <div class="toctitle" lang="en" dir="ltr"> <h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span> </div> <ul> <li class="toclevel-1 tocsection-1"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Definition_and_properties"><span class="tocnumber">1</span> <span class="toctext">Definition and properties</span></a> <ul> <li class="toclevel-2 tocsection-2"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Average_acceleration"><span class="tocnumber">1.1</span> <span class="toctext">Average acceleration</span></a></li> <li class="toclevel-2 tocsection-3"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Instantaneous_acceleration"><span class="tocnumber">1.2</span> <span class="toctext">Instantaneous acceleration</span></a></li> <li class="toclevel-2 tocsection-4"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Units"><span class="tocnumber">1.3</span> <span class="toctext">Units</span></a></li> <li class="toclevel-2 tocsection-5"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Other_forms"><span class="tocnumber">1.4</span> <span class="toctext">Other forms</span></a></li> </ul></li> <li class="toclevel-1 tocsection-6"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Tangential_and_centripetal_acceleration"><span class="tocnumber">2</span> <span class="toctext">Tangential and centripetal acceleration</span></a></li> <li class="toclevel-1 tocsection-7"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Special_cases"><span class="tocnumber">3</span> <span class="toctext">Special cases</span></a> <ul> <li class="toclevel-2 tocsection-8"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Uniform_acceleration"><span class="tocnumber">3.1</span> <span class="toctext">Uniform acceleration</span></a></li> <li class="toclevel-2 tocsection-9"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Circular_motion"><span class="tocnumber">3.2</span> <span class="toctext">Circular motion</span></a></li> </ul></li> <li class="toclevel-1 tocsection-10"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Coordinate_systems"><span class="tocnumber">4</span> <span class="toctext">Coordinate systems</span></a></li> <li class="toclevel-1 tocsection-11"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Relation_to_relativity"><span class="tocnumber">5</span> <span class="toctext">Relation to relativity</span></a> <ul> <li class="toclevel-2 tocsection-12"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Special_relativity"><span class="tocnumber">5.1</span> <span class="toctext">Special relativity</span></a></li> <li class="toclevel-2 tocsection-13"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#General_relativity"><span class="tocnumber">5.2</span> <span class="toctext">General relativity</span></a></li> </ul></li> <li class="toclevel-1 tocsection-14"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Conversions"><span class="tocnumber">6</span> <span class="toctext">Conversions</span></a></li> <li class="toclevel-1 tocsection-15"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#See_also"><span class="tocnumber">7</span> <span class="toctext">See also</span></a></li> <li class="toclevel-1 tocsection-16"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#References"><span class="tocnumber">8</span> <span class="toctext">References</span></a></li> <li class="toclevel-1 tocsection-17"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#External_links"><span class="tocnumber">9</span> <span class="toctext">External links</span></a></li> </ul> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Definition_and_properties">Definition and properties</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=1&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Definition and properties" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-1 collapsible-block" id="mf-section-1"> <figure typeof="mw:File/Thumb"> <a href="https://en-m-wikipedia-org.translate.goog/wiki/File:Kinematics.svg?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Kinematics.svg/300px-Kinematics.svg.png" decoding="async" width="300" height="181" class="mw-file-element" data-file-width="524" data-file-height="317"> </noscript><span class="lazy-image-placeholder" style="width: 300px;height: 181px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Kinematics.svg/300px-Kinematics.svg.png" data-width="300" data-height="181" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Kinematics.svg/450px-Kinematics.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Kinematics.svg/600px-Kinematics.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption> Kinematic quantities of a classical particle: mass <span class="texhtml mvar" style="font-style:italic;">m</span>, position <span class="texhtml"><b>r</b></span>, velocity <span class="texhtml"><b>v</b></span>, acceleration <span class="texhtml"><b>a</b></span>. </figcaption> </figure> <div class="mw-heading mw-heading3"> <h3 id="Average_acceleration">Average acceleration</h3><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=2&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Average acceleration" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"> <a href="https://en-m-wikipedia-org.translate.goog/wiki/File:Acceleration_as_derivative_of_velocity_along_trajectory.svg?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Acceleration_as_derivative_of_velocity_along_trajectory.svg/220px-Acceleration_as_derivative_of_velocity_along_trajectory.svg.png" decoding="async" width="220" height="170" class="mw-file-element" data-file-width="705" data-file-height="545"> </noscript><span class="lazy-image-placeholder" style="width: 220px;height: 170px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Acceleration_as_derivative_of_velocity_along_trajectory.svg/220px-Acceleration_as_derivative_of_velocity_along_trajectory.svg.png" data-width="220" data-height="170" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Acceleration_as_derivative_of_velocity_along_trajectory.svg/330px-Acceleration_as_derivative_of_velocity_along_trajectory.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Acceleration_as_derivative_of_velocity_along_trajectory.svg/440px-Acceleration_as_derivative_of_velocity_along_trajectory.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption> Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction at that point. The true acceleration at time <span class="texhtml mvar" style="font-style:italic;">t</span> is found in the limit as <a href="https://en-m-wikipedia-org.translate.goog/wiki/Time_interval?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Time interval">time interval</a> <span class="texhtml">Δ<i>t</i> → 0</span> of <span class="texhtml">Δ<b>v</b>/Δ<i>t</i></span>. </figcaption> </figure> <p>An object's average acceleration over a period of <a href="https://en-m-wikipedia-org.translate.goog/wiki/Time_in_physics?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Time in physics">time</a> is its change in <a href="https://en-m-wikipedia-org.translate.goog/wiki/Velocity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Velocity">velocity</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 \Delta \mathbf {v} }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal"> Δ<!-- Δ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \Delta \mathbf {v} } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ae2621f980eefffc0a3f3e806bfce57a5be867a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.347ex; height:2.176ex;" alt="{\displaystyle \Delta \mathbf {v} }"> </noscript><span class="lazy-image-placeholder" style="width: 3.347ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ae2621f980eefffc0a3f3e806bfce57a5be867a" data-alt="{\displaystyle \Delta \mathbf {v} }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, divided by the duration of the period, <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<!-- Δ --> </mi> <mi> t </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \Delta t} </annotation> </semantics> </math></span> <noscript> <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}"> </noscript><span class="lazy-image-placeholder" style="width: 2.775ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c28867ecd34e2caed12cf38feadf6a81a7ee542" data-alt="{\displaystyle \Delta t}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>. Mathematically, <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {\mathbf {a} }}={\frac {\Delta \mathbf {v} }{\Delta t}}.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mo stretchy="false"> ¯<!-- ¯ --> </mo> </mover> </mrow> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal"> Δ<!-- Δ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> </mrow> <mrow> <mi mathvariant="normal"> Δ<!-- Δ --> </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\bar {\mathbf {a} }}={\frac {\Delta \mathbf {v} }{\Delta t}}.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/941bc4c58dbc6f6716ce1d0024ff29e2ee82a0c9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.228ex; height:5.509ex;" alt="{\displaystyle {\bar {\mathbf {a} }}={\frac {\Delta \mathbf {v} }{\Delta t}}.}"> </noscript><span class="lazy-image-placeholder" style="width: 9.228ex;height: 5.509ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/941bc4c58dbc6f6716ce1d0024ff29e2ee82a0c9" data-alt="{\displaystyle {\bar {\mathbf {a} }}={\frac {\Delta \mathbf {v} }{\Delta t}}.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span></p> <div class="mw-heading mw-heading3"> <h3 id="Instantaneous_acceleration">Instantaneous acceleration</h3><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=3&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Instantaneous acceleration" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"> <a href="https://en-m-wikipedia-org.translate.goog/wiki/File:1-D_kinematics.svg?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/1-D_kinematics.svg/220px-1-D_kinematics.svg.png" decoding="async" width="220" height="232" class="mw-file-element" data-file-width="445" data-file-height="470"> </noscript><span class="lazy-image-placeholder" style="width: 220px;height: 232px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/1-D_kinematics.svg/220px-1-D_kinematics.svg.png" data-width="220" data-height="232" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/1-D_kinematics.svg/330px-1-D_kinematics.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/1-D_kinematics.svg/440px-1-D_kinematics.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption> <b>From bottom to top</b>: <div> <ul> <li>an acceleration function <span class="texhtml"><i>a</i>(<i>t</i>)</span>;</li> <li>the integral of the acceleration is the velocity function <span class="texhtml"><i>v</i>(<i>t</i>)</span>;</li> <li>and the integral of the velocity is the distance function <span class="texhtml"><i>s</i>(<i>t</i>)</span>.</li> </ul> </div> </figcaption> </figure> <p>Instantaneous acceleration, meanwhile, is the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Limit_of_a_function?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Limit of a function">limit</a> of the average acceleration over an <a href="https://en-m-wikipedia-org.translate.goog/wiki/Infinitesimal?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Infinitesimal">infinitesimal</a> interval of time. In the terms of <a href="https://en-m-wikipedia-org.translate.goog/wiki/Calculus?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Calculus">calculus</a>, instantaneous acceleration is the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Derivative?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Derivative">derivative</a> of the velocity vector with respect to time: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {a} =\lim _{{\Delta t}\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {d\mathbf {v} }{dt}}.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mo> = </mo> <munder> <mo movablelimits="true" form="prefix"> lim </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> Δ<!-- Δ --> </mi> <mi> t </mi> </mrow> <mo stretchy="false"> →<!-- → --> </mo> <mn> 0 </mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal"> Δ<!-- Δ --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> </mrow> <mrow> <mi mathvariant="normal"> Δ<!-- Δ --> </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {a} =\lim _{{\Delta t}\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {d\mathbf {v} }{dt}}.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d545c82c8f7f22605abdb6b1b9d2605583e819a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:20.604ex; height:5.676ex;" alt="{\displaystyle \mathbf {a} =\lim _{{\Delta t}\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {d\mathbf {v} }{dt}}.}"> </noscript><span class="lazy-image-placeholder" style="width: 20.604ex;height: 5.676ex;vertical-align: -2.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d545c82c8f7f22605abdb6b1b9d2605583e819a" data-alt="{\displaystyle \mathbf {a} =\lim _{{\Delta t}\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {d\mathbf {v} }{dt}}.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span> As acceleration is defined as the derivative of velocity, <span class="texhtml"><b>v</b></span>, with respect to time <span class="texhtml mvar" style="font-style:italic;">t</span> and velocity is defined as the derivative of position, <span class="texhtml"><b>x</b></span>, with respect to time, acceleration can be thought of as the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Second_derivative?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Second derivative">second derivative</a> of <span class="texhtml"><b>x</b></span> with respect to <span class="texhtml mvar" style="font-style:italic;">t</span>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> x </mi> </mrow> </mrow> <mrow> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99cc6821e0ed27be073066484854b6ceaa22ddfc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.126ex; height:6.009ex;" alt="{\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}.}"> </noscript><span class="lazy-image-placeholder" style="width: 16.126ex;height: 6.009ex;vertical-align: -2.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99cc6821e0ed27be073066484854b6ceaa22ddfc" data-alt="{\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span></p> <p>(Here and elsewhere, if <a href="https://en-m-wikipedia-org.translate.goog/wiki/Rectilinear_motion?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Rectilinear motion">motion is in a straight line</a>, <a href="https://en-m-wikipedia-org.translate.goog/wiki/Euclidean_vector?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Euclidean vector">vector</a> quantities can be substituted by <a href="https://en-m-wikipedia-org.translate.goog/wiki/Scalar_(physics)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Scalar (physics)">scalars</a> in the equations.)</p> <p>By the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Fundamental_theorem_of_calculus?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Fundamental theorem of calculus">fundamental theorem of calculus</a>, it can be seen that the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Integral?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Integral">integral</a> of the acceleration function <span class="texhtml"><i>a</i>(<i>t</i>)</span> is the velocity function <span class="texhtml"><i>v</i>(<i>t</i>)</span>; that is, the area under the curve of an acceleration vs. time (<span class="texhtml mvar" style="font-style:italic;">a</span> vs. <span class="texhtml mvar" style="font-style:italic;">t</span>) graph corresponds to the change of velocity. <span class="mwe-math-element" data-qid="Q11465"><a href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Special:MathWikibase&qid=Q11465&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" style="color:inherit;"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {\Delta v} =\int \mathbf {a} \,dt.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> Δ<!-- Δ --> </mi> <mi mathvariant="bold"> v </mi> </mrow> <mo> = </mo> <mo> ∫<!-- ∫ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mspace width="thinmathspace"></mspace> <mi> d </mi> <mi> t </mi> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {\Delta v} =\int \mathbf {a} \,dt.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f073fed8813863277c4736356f81b20bef43d72" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.705ex; height:5.676ex;" alt="{\displaystyle \mathbf {\Delta v} =\int \mathbf {a} \,dt.}"> </noscript><span class="lazy-image-placeholder" style="width: 13.705ex;height: 5.676ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f073fed8813863277c4736356f81b20bef43d72" data-alt="{\displaystyle \mathbf {\Delta v} =\int \mathbf {a} \,dt.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></a></span></p> <p>Likewise, the integral of the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Jerk_(physics)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Jerk (physics)">jerk</a> function <span class="texhtml"><i>j</i>(<i>t</i>)</span>, the derivative of the acceleration function, can be used to find the change of acceleration at a certain time: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {\Delta a} =\int \mathbf {j} \,dt.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> Δ<!-- Δ --> </mi> <mi mathvariant="bold"> a </mi> </mrow> <mo> = </mo> <mo> ∫<!-- ∫ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> j </mi> </mrow> <mspace width="thinmathspace"></mspace> <mi> d </mi> <mi> t </mi> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {\Delta a} =\int \mathbf {j} \,dt.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ecbc1f7e6ae184700b69b478abe2abb42939c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.111ex; height:5.676ex;" alt="{\displaystyle \mathbf {\Delta a} =\int \mathbf {j} \,dt.}"> </noscript><span class="lazy-image-placeholder" style="width: 13.111ex;height: 5.676ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ecbc1f7e6ae184700b69b478abe2abb42939c" data-alt="{\displaystyle \mathbf {\Delta a} =\int \mathbf {j} \,dt.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span></p> <div class="mw-heading mw-heading3"> <h3 id="Units">Units</h3><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=4&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Units" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>Acceleration has the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Dimensional_analysis?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Dimensional analysis">dimensions</a> of velocity (L/T) divided by time, i.e. <a href="https://en-m-wikipedia-org.translate.goog/wiki/Length?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Length">L</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Time?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Time">T</a><sup>−2</sup>. The <a href="https://en-m-wikipedia-org.translate.goog/wiki/International_System_of_Units?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="International System of Units">SI</a> unit of acceleration is the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Metre_per_second_squared?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Metre per second squared">metre per second squared</a> (m s<sup>−2</sup>); or "metre per second per second", as the velocity in metres per second changes by the acceleration value, every second.</p> <div class="mw-heading mw-heading3"> <h3 id="Other_forms">Other forms</h3><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=5&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Other forms" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <p>An object moving in a circular motion—such as a satellite orbiting the Earth—is accelerating due to the change of direction of motion, although its speed may be constant. In this case it is said to be undergoing <i>centripetal</i> (directed towards the center) acceleration.</p> <p><a href="https://en-m-wikipedia-org.translate.goog/wiki/Proper_acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Proper acceleration">Proper acceleration</a>, the acceleration of a body relative to a free-fall condition, is measured by an instrument called an <a href="https://en-m-wikipedia-org.translate.goog/wiki/Accelerometer?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Accelerometer">accelerometer</a>.</p> <p>In <a href="https://en-m-wikipedia-org.translate.goog/wiki/Classical_mechanics?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Classical mechanics">classical mechanics</a>, for a body with constant mass, the (vector) acceleration of the body's center of mass is proportional to the net <a href="https://en-m-wikipedia-org.translate.goog/wiki/Force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Force">force</a> vector (i.e. sum of all forces) acting on it (<a href="https://en-m-wikipedia-org.translate.goog/wiki/Newton%27s_laws_of_motion?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Newton's_second_law" title="Newton's laws of motion">Newton's second law</a>): <span class="mwe-math-element" data-qid="Q2397319"><a href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Special:MathWikibase&qid=Q2397319&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" style="color:inherit;"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F} =m\mathbf {a} \quad \implies \quad \mathbf {a} ={\frac {\mathbf {F} }{m}},}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mo> = </mo> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mspace width="1em"></mspace> <mspace width="thickmathspace"></mspace> <mo stretchy="false"> ⟹<!-- ⟹ --> </mo> <mspace width="thickmathspace"></mspace> <mspace width="1em"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> F </mi> </mrow> <mi> m </mi> </mfrac> </mrow> <mo> , </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {F} =m\mathbf {a} \quad \implies \quad \mathbf {a} ={\frac {\mathbf {F} }{m}},} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5c0d3abfa63b485b95bf50c8938c73736982547" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:27.074ex; height:5.176ex;" alt="{\displaystyle \mathbf {F} =m\mathbf {a} \quad \implies \quad \mathbf {a} ={\frac {\mathbf {F} }{m}},}"> </noscript><span class="lazy-image-placeholder" style="width: 27.074ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5c0d3abfa63b485b95bf50c8938c73736982547" data-alt="{\displaystyle \mathbf {F} =m\mathbf {a} \quad \implies \quad \mathbf {a} ={\frac {\mathbf {F} }{m}},}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></a></span> where <span class="texhtml"><b>F</b></span> is the net force acting on the body, <span class="texhtml mvar" style="font-style:italic;">m</span> is the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Mass?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Mass">mass</a> of the body, and <span class="texhtml"><b>a</b></span> is the center-of-mass acceleration. As speeds approach the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Speed_of_light?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Speed of light">speed of light</a>, <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special_relativity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special relativity">relativistic effects</a> become increasingly large.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Tangential_and_centripetal_acceleration">Tangential and centripetal acceleration</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=6&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Tangential and centripetal acceleration" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-2 collapsible-block" id="mf-section-2"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"> <div role="note" class="hatnote navigation-not-searchable"> See also: <a href="https://en-m-wikipedia-org.translate.goog/wiki/Centripetal_force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Local_coordinates" title="Centripetal force">Centripetal force § Local coordinates</a>, and <a href="https://en-m-wikipedia-org.translate.goog/wiki/Tangential_velocity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Tangential velocity">Tangential velocity</a> </div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"> <a href="https://en-m-wikipedia-org.translate.goog/wiki/File:Oscillating_pendulum.gif?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Oscillating_pendulum.gif/220px-Oscillating_pendulum.gif" decoding="async" width="220" height="206" class="mw-file-element" data-file-width="341" data-file-height="320"> </noscript><span class="lazy-image-placeholder" style="width: 220px;height: 206px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Oscillating_pendulum.gif/220px-Oscillating_pendulum.gif" data-width="220" data-height="206" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Oscillating_pendulum.gif/330px-Oscillating_pendulum.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/2/24/Oscillating_pendulum.gif 2x" data-class="mw-file-element"> </span></a> <figcaption> An oscillating pendulum, with velocity and acceleration marked. It experiences both tangential and centripetal acceleration. </figcaption> </figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"> <a href="https://en-m-wikipedia-org.translate.goog/wiki/File:Acceleration_components.svg?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Acceleration_components.svg/220px-Acceleration_components.svg.png" decoding="async" width="220" height="145" class="mw-file-element" data-file-width="512" data-file-height="338"> </noscript><span class="lazy-image-placeholder" style="width: 220px;height: 145px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Acceleration_components.svg/220px-Acceleration_components.svg.png" data-width="220" data-height="145" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Acceleration_components.svg/330px-Acceleration_components.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/45/Acceleration_components.svg/440px-Acceleration_components.svg.png 2x" data-class="mw-file-element"> </span></a> <figcaption> Components of acceleration for a curved motion. The tangential component <span class="texhtml"><b>a</b><sub>t</sub></span> is due to the change in speed of traversal, and points along the curve in the direction of the velocity vector (or in the opposite direction). The normal component (also called centripetal component for circular motion) <span class="texhtml"><b>a</b><sub>c</sub></span> is due to the change in direction of the velocity vector and is normal to the trajectory, pointing toward the center of curvature of the path. </figcaption> </figure> <p>The velocity of a particle moving on a curved path as a <a href="https://en-m-wikipedia-org.translate.goog/wiki/Function_(mathematics)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Function (mathematics)">function</a> of time can be written as: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {v} (t)=v(t){\frac {\mathbf {v} (t)}{v(t)}}=v(t)\mathbf {u} _{\mathrm {t} }(t),}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> = </mo> <mi> v </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mrow> <mrow> <mi> v </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mrow> </mfrac> </mrow> <mo> = </mo> <mi> v </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> u </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> t </mi> </mrow> </mrow> </msub> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> , </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {v} (t)=v(t){\frac {\mathbf {v} (t)}{v(t)}}=v(t)\mathbf {u} _{\mathrm {t} }(t),} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b4ed403ef705caf6d21e5f0c64cdd6b78407da8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:28.359ex; height:6.509ex;" alt="{\displaystyle \mathbf {v} (t)=v(t){\frac {\mathbf {v} (t)}{v(t)}}=v(t)\mathbf {u} _{\mathrm {t} }(t),}"> </noscript><span class="lazy-image-placeholder" style="width: 28.359ex;height: 6.509ex;vertical-align: -2.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b4ed403ef705caf6d21e5f0c64cdd6b78407da8" data-alt="{\displaystyle \mathbf {v} (t)=v(t){\frac {\mathbf {v} (t)}{v(t)}}=v(t)\mathbf {u} _{\mathrm {t} }(t),}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span> with <span class="texhtml"><i>v</i>(<i>t</i>)</span> equal to the speed of travel along the path, and <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {u} _{\mathrm {t} }={\frac {\mathbf {v} (t)}{v(t)}}\,,}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> u </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> t </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mrow> <mrow> <mi> v </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mo> , </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {u} _{\mathrm {t} }={\frac {\mathbf {v} (t)}{v(t)}}\,,} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f24d17c9f66ed44e8a21b0f1c30f332ca59edb2e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:11.386ex; height:6.509ex;" alt="{\displaystyle \mathbf {u} _{\mathrm {t} }={\frac {\mathbf {v} (t)}{v(t)}}\,,}"> </noscript><span class="lazy-image-placeholder" style="width: 11.386ex;height: 6.509ex;vertical-align: -2.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f24d17c9f66ed44e8a21b0f1c30f332ca59edb2e" data-alt="{\displaystyle \mathbf {u} _{\mathrm {t} }={\frac {\mathbf {v} (t)}{v(t)}}\,,}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span> a <a href="https://en-m-wikipedia-org.translate.goog/wiki/Differential_geometry_of_curves?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Tangent_vector" class="mw-redirect" title="Differential geometry of curves">unit vector tangent</a> to the path pointing in the direction of motion at the chosen moment in time. Taking into account both the changing speed <span class="texhtml"><i>v</i>(<i>t</i>)</span> and the changing direction of <span class="texhtml"><b>u</b><sub><i>t</i></sub></span>, the acceleration of a particle moving on a curved path can be written using the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Chain_rule?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Chain rule">chain rule</a> of differentiation<sup id="cite_ref-7" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> for the product of two functions of time as:</p> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{alignedat}{3}\mathbf {a} &={\frac {d\mathbf {v} }{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+v(t){\frac {d\mathbf {u} _{\mathrm {t} }}{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+{\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }\ ,\end{alignedat}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left" rowspacing="3pt" columnspacing="0em 0em 0em 0em 0em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> </mtd> <mtd> <mi></mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mi></mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mi> v </mi> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> u </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> t </mi> </mrow> </mrow> </msub> <mo> + </mo> <mi> v </mi> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> u </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> t </mi> </mrow> </mrow> </msub> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd></mtd> <mtd> <mi></mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mi> v </mi> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> u </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> t </mi> </mrow> </mrow> </msub> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> r </mi> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> u </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> n </mi> </mrow> </mrow> </msub> <mtext> </mtext> <mo> , </mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\begin{alignedat}{3}\mathbf {a} &={\frac {d\mathbf {v} }{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+v(t){\frac {d\mathbf {u} _{\mathrm {t} }}{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+{\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }\ ,\end{alignedat}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49a88fa2cf023a1cac99133acfed8d7961e07c0b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -7.838ex; width:21.712ex; height:16.843ex;" alt="{\displaystyle {\begin{alignedat}{3}\mathbf {a} &={\frac {d\mathbf {v} }{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+v(t){\frac {d\mathbf {u} _{\mathrm {t} }}{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+{\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }\ ,\end{alignedat}}}"> </noscript><span class="lazy-image-placeholder" style="width: 21.712ex;height: 16.843ex;vertical-align: -7.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49a88fa2cf023a1cac99133acfed8d7961e07c0b" data-alt="{\displaystyle {\begin{alignedat}{3}\mathbf {a} &={\frac {d\mathbf {v} }{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+v(t){\frac {d\mathbf {u} _{\mathrm {t} }}{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+{\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }\ ,\end{alignedat}}}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span></p> <p>where <span class="texhtml"><b>u</b><sub>n</sub></span> is the unit (inward) <a href="https://en-m-wikipedia-org.translate.goog/wiki/Differential_geometry_of_curves?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Normal_or_curvature_vector" class="mw-redirect" title="Differential geometry of curves">normal vector</a> to the particle's trajectory (also called <i>the principal normal</i>), and <span class="texhtml"><b>r</b></span> is its instantaneous <a href="https://en-m-wikipedia-org.translate.goog/wiki/Curvature?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Curvature_of_plane_curves" title="Curvature">radius of curvature</a> based upon the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Osculating_circle?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#Mathematical_description" title="Osculating circle">osculating circle</a> at time <span class="texhtml mvar" style="font-style:italic;">t</span>. The components</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 \mathbf {a} _{\mathrm {t} }={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }\quad {\text{and}}\quad \mathbf {a} _{\mathrm {c} }={\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> t </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi> d </mi> <mi> v </mi> </mrow> <mrow> <mi> d </mi> <mi> t </mi> </mrow> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> u </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> t </mi> </mrow> </mrow> </msub> <mspace width="1em"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mtext> and </mtext> </mrow> <mspace width="1em"></mspace> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> c </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> r </mi> </mfrac> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> u </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> n </mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {a} _{\mathrm {t} }={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }\quad {\text{and}}\quad \mathbf {a} _{\mathrm {c} }={\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cc7ccce3437ffaa274f0018f50b895faa209dd1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:30.209ex; height:5.843ex;" alt="{\displaystyle \mathbf {a} _{\mathrm {t} }={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }\quad {\text{and}}\quad \mathbf {a} _{\mathrm {c} }={\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }}"> </noscript><span class="lazy-image-placeholder" style="width: 30.209ex;height: 5.843ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cc7ccce3437ffaa274f0018f50b895faa209dd1" data-alt="{\displaystyle \mathbf {a} _{\mathrm {t} }={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }\quad {\text{and}}\quad \mathbf {a} _{\mathrm {c} }={\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>are called the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Tangential_acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Tangential acceleration">tangential acceleration</a> and the normal or radial acceleration (or centripetal acceleration in circular motion, see also <a href="https://en-m-wikipedia-org.translate.goog/wiki/Circular_motion?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Circular motion">circular motion</a> and <a href="https://en-m-wikipedia-org.translate.goog/wiki/Centripetal_force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Centripetal force">centripetal force</a>), respectively.</p> <p>Geometrical analysis of three-dimensional space curves, which explains tangent, (principal) normal and binormal, is described by the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Frenet%E2%80%93Serret_formulas?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Frenet–Serret formulas">Frenet–Serret formulas</a>.<sup id="cite_ref-Andrews_8-0" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-Andrews-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Chand_9-0" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-Chand-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Special_cases">Special cases</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=7&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Special cases" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-3 collapsible-block" id="mf-section-3"> <div class="mw-heading mw-heading3"> <h3 id="Uniform_acceleration">Uniform acceleration</h3><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=8&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Uniform acceleration" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"> <div role="note" class="hatnote navigation-not-searchable"> See also: <a href="https://en-m-wikipedia-org.translate.goog/wiki/Torricelli%27s_equation?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Torricelli's equation">Torricelli's equation</a> </div> <figure class="mw-default-size" typeof="mw:File/Thumb"> <a href="https://en-m-wikipedia-org.translate.goog/wiki/File:Strecke_und_konstante_Beschleunigung.png?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Strecke_und_konstante_Beschleunigung.png/220px-Strecke_und_konstante_Beschleunigung.png" decoding="async" width="220" height="170" class="mw-file-element" data-file-width="403" data-file-height="311"> </noscript><span class="lazy-image-placeholder" style="width: 220px;height: 170px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Strecke_und_konstante_Beschleunigung.png/220px-Strecke_und_konstante_Beschleunigung.png" data-width="220" data-height="170" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Strecke_und_konstante_Beschleunigung.png/330px-Strecke_und_konstante_Beschleunigung.png 1.5x, //upload.wikimedia.org/wikipedia/commons/f/fe/Strecke_und_konstante_Beschleunigung.png 2x" data-class="mw-file-element"> </span></a> <figcaption> Calculation of the speed difference for a uniform acceleration </figcaption> </figure> <p><i>Uniform</i> or <i>constant</i> acceleration is a type of motion in which the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Velocity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Velocity">velocity</a> of an object changes by an equal amount in every equal time period.</p> <p>A frequently cited example of uniform acceleration is that of an object in <a href="https://en-m-wikipedia-org.translate.goog/wiki/Free_fall?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Free fall">free fall</a> in a uniform gravitational field. The acceleration of a falling body in the absence of resistances to motion is dependent only on the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Gravitational_field?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Gravitational field">gravitational field</a> strength <a href="https://en-m-wikipedia-org.translate.goog/wiki/Standard_gravity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Standard gravity"><span class="texhtml">g</span></a> (also called <i>acceleration due to gravity</i>). By <a href="https://en-m-wikipedia-org.translate.goog/wiki/Newton%27s_Second_Law?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Newton's Second Law">Newton's Second Law</a> the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Force">force</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 \mathbf {F_{g}} }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold"> F </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> g </mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {F_{g}} } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63d24e9fb0bb3ba45643f3e889d122827f6ac039" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.86ex; height:2.843ex;" alt="{\displaystyle \mathbf {F_{g}} }"> </noscript><span class="lazy-image-placeholder" style="width: 2.86ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63d24e9fb0bb3ba45643f3e889d122827f6ac039" data-alt="{\displaystyle \mathbf {F_{g}} }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> acting on a body is given by: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {F_{g}} =m\mathbf {g} .}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold"> F </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> g </mi> </mrow> </msub> </mrow> <mo> = </mo> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> g </mi> </mrow> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {F_{g}} =m\mathbf {g} .} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12599046436c678a919c8a59f938c218b0c397d3" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.982ex; height:2.843ex;" alt="{\displaystyle \mathbf {F_{g}} =m\mathbf {g} .}"> </noscript><span class="lazy-image-placeholder" style="width: 9.982ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12599046436c678a919c8a59f938c218b0c397d3" data-alt="{\displaystyle \mathbf {F_{g}} =m\mathbf {g} .}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span></p> <p>Because of the simple analytic properties of the case of constant acceleration, there are simple formulas relating the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Displacement_(vector)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Displacement (vector)">displacement</a>, initial and time-dependent <a href="https://en-m-wikipedia-org.translate.goog/wiki/Velocity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Velocity">velocities</a>, and acceleration to the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Time_in_physics?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Time in physics">time elapsed</a>:<sup id="cite_ref-10" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\mathbf {s} (t)&=\mathbf {s} _{0}+\mathbf {v} _{0}t+{\tfrac {1}{2}}\mathbf {a} t^{2}=\mathbf {s} _{0}+{\tfrac {1}{2}}\left(\mathbf {v} _{0}+\mathbf {v} (t)\right)t\\\mathbf {v} (t)&=\mathbf {v} _{0}+\mathbf {a} t\\{v^{2}}(t)&={v_{0}}^{2}+2\mathbf {a\cdot } [\mathbf {s} (t)-\mathbf {s} _{0}],\end{aligned}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> s </mi> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mtd> <mtd> <mi></mi> <mo> = </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> s </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> + </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mi> t </mi> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> = </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> s </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mstyle> </mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mrow> <mo> ) </mo> </mrow> <mi> t </mi> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mtd> <mtd> <mi></mi> <mo> = </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> <mi> t </mi> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mtd> <mtd> <mi></mi> <mo> = </mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <mn> 2 </mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> <mo> ⋅<!-- ⋅ --> </mo> </mrow> <mo stretchy="false"> [ </mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> s </mi> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> <mo> −<!-- − --> </mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> s </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> <mo stretchy="false"> ] </mo> <mo> , </mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\begin{aligned}\mathbf {s} (t)&=\mathbf {s} _{0}+\mathbf {v} _{0}t+{\tfrac {1}{2}}\mathbf {a} t^{2}=\mathbf {s} _{0}+{\tfrac {1}{2}}\left(\mathbf {v} _{0}+\mathbf {v} (t)\right)t\\\mathbf {v} (t)&=\mathbf {v} _{0}+\mathbf {a} t\\{v^{2}}(t)&={v_{0}}^{2}+2\mathbf {a\cdot } [\mathbf {s} (t)-\mathbf {s} _{0}],\end{aligned}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5bad5bdcb976c98a24324c4f4abd4a3cce7e6fa" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:47.123ex; height:10.176ex;" alt="{\displaystyle {\begin{aligned}\mathbf {s} (t)&=\mathbf {s} _{0}+\mathbf {v} _{0}t+{\tfrac {1}{2}}\mathbf {a} t^{2}=\mathbf {s} _{0}+{\tfrac {1}{2}}\left(\mathbf {v} _{0}+\mathbf {v} (t)\right)t\\\mathbf {v} (t)&=\mathbf {v} _{0}+\mathbf {a} t\\{v^{2}}(t)&={v_{0}}^{2}+2\mathbf {a\cdot } [\mathbf {s} (t)-\mathbf {s} _{0}],\end{aligned}}}"> </noscript><span class="lazy-image-placeholder" style="width: 47.123ex;height: 10.176ex;vertical-align: -4.505ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5bad5bdcb976c98a24324c4f4abd4a3cce7e6fa" data-alt="{\displaystyle {\begin{aligned}\mathbf {s} (t)&=\mathbf {s} _{0}+\mathbf {v} _{0}t+{\tfrac {1}{2}}\mathbf {a} t^{2}=\mathbf {s} _{0}+{\tfrac {1}{2}}\left(\mathbf {v} _{0}+\mathbf {v} (t)\right)t\\\mathbf {v} (t)&=\mathbf {v} _{0}+\mathbf {a} t\\{v^{2}}(t)&={v_{0}}^{2}+2\mathbf {a\cdot } [\mathbf {s} (t)-\mathbf {s} _{0}],\end{aligned}}}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span></p> <p>where</p> <ul> <li><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> <noscript> <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}"> </noscript><span class="lazy-image-placeholder" style="width: 0.84ex;height: 2.009ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" data-alt="{\displaystyle t}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the elapsed time,</li> <li><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 \mathbf {s} _{0}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> s </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {s} _{0}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f0bd2e93a5e3dd1ebd7fc7d1efbad1cf1a916aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.11ex; height:2.009ex;" alt="{\displaystyle \mathbf {s} _{0}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.11ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f0bd2e93a5e3dd1ebd7fc7d1efbad1cf1a916aa" data-alt="{\displaystyle \mathbf {s} _{0}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the initial displacement from the origin,</li> <li><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 \mathbf {s} (t)}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> s </mi> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {s} (t)} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fde0f017af7e73213f4726ead5baf36a0512260b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.705ex; height:2.843ex;" alt="{\displaystyle \mathbf {s} (t)}"> </noscript><span class="lazy-image-placeholder" style="width: 3.705ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fde0f017af7e73213f4726ead5baf36a0512260b" data-alt="{\displaystyle \mathbf {s} (t)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the displacement from the origin at time <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> <noscript> <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}"> </noscript><span class="lazy-image-placeholder" style="width: 0.84ex;height: 2.009ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" data-alt="{\displaystyle t}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>,</li> <li><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 \mathbf {v} _{0}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 0 </mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {v} _{0}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ace1ee3c9fc209269fe95de85fb09c25823dd1e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.465ex; height:2.009ex;" alt="{\displaystyle \mathbf {v} _{0}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.465ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ace1ee3c9fc209269fe95de85fb09c25823dd1e4" data-alt="{\displaystyle \mathbf {v} _{0}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the initial velocity,</li> <li><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 \mathbf {v} (t)}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> v </mi> </mrow> <mo stretchy="false"> ( </mo> <mi> t </mi> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {v} (t)} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee594765ca30167f80394d3349307a445782d012" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.06ex; height:2.843ex;" alt="{\displaystyle \mathbf {v} (t)}"> </noscript><span class="lazy-image-placeholder" style="width: 4.06ex;height: 2.843ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee594765ca30167f80394d3349307a445782d012" data-alt="{\displaystyle \mathbf {v} (t)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the velocity at time <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> <noscript> <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}"> </noscript><span class="lazy-image-placeholder" style="width: 0.84ex;height: 2.009ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" data-alt="{\displaystyle t}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, and</li> <li><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 \mathbf {a} }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> a </mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {a} } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a957216653a9ee0d0133dcefd13fb75e36b8b9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.299ex; height:1.676ex;" alt="{\displaystyle \mathbf {a} }"> </noscript><span class="lazy-image-placeholder" style="width: 1.299ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a957216653a9ee0d0133dcefd13fb75e36b8b9d" data-alt="{\displaystyle \mathbf {a} }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is the uniform rate of acceleration.</li> </ul> <p>In particular, the motion can be resolved into two orthogonal parts, one of constant velocity and the other according to the above equations. As <a href="https://en-m-wikipedia-org.translate.goog/wiki/Galileo?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Galileo">Galileo</a> showed, the net result is parabolic motion, which describes, e.g., the trajectory of a projectile in vacuum near the surface of Earth.<sup id="cite_ref-11" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></p> <div class="mw-heading mw-heading3"> <h3 id="Circular_motion">Circular motion</h3><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=9&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Circular motion" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style> <div class="thumb tmulti tright"> <div class="thumbinner multiimageinner" style="width:462px;max-width:462px"> <div class="trow"> <div class="tsingle" style="width:102px;max-width:102px"> <div class="thumbimage"> <span typeof="mw:File"><a href="https://en-m-wikipedia-org.translate.goog/wiki/File:Position_vector_plane_polar_coords.svg?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"> <noscript> <img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Position_vector_plane_polar_coords.svg/100px-Position_vector_plane_polar_coords.svg.png" decoding="async" width="100" height="137" class="mw-file-element" data-file-width="155" data-file-height="212"> </noscript><span class="lazy-image-placeholder" style="width: 100px;height: 137px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Position_vector_plane_polar_coords.svg/100px-Position_vector_plane_polar_coords.svg.png" data-alt="" data-width="100" data-height="137" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Position_vector_plane_polar_coords.svg/150px-Position_vector_plane_polar_coords.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Position_vector_plane_polar_coords.svg/200px-Position_vector_plane_polar_coords.svg.png 2x" data-class="mw-file-element"> </span></a></span> </div> <div class="thumbcaption"> Position vector <b>r</b>, always points radially from the origin. </div> </div> <div class="tsingle" style="width:152px;max-width:152px"> <div class="thumbimage"> <span typeof="mw:File"><a href="https://en-m-wikipedia-org.translate.goog/wiki/File:Velocity_vector_plane_polar_coords.svg?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"> <noscript> <img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Velocity_vector_plane_polar_coords.svg/150px-Velocity_vector_plane_polar_coords.svg.png" decoding="async" width="150" height="125" class="mw-file-element" data-file-width="255" data-file-height="212"> </noscript><span class="lazy-image-placeholder" style="width: 150px;height: 125px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Velocity_vector_plane_polar_coords.svg/150px-Velocity_vector_plane_polar_coords.svg.png" data-alt="" data-width="150" data-height="125" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Velocity_vector_plane_polar_coords.svg/225px-Velocity_vector_plane_polar_coords.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Velocity_vector_plane_polar_coords.svg/300px-Velocity_vector_plane_polar_coords.svg.png 2x" data-class="mw-file-element"> </span></a></span> </div> <div class="thumbcaption"> Velocity vector <b>v</b>, always tangent to the path of motion. </div> </div> <div class="tsingle" style="width:202px;max-width:202px"> <div class="thumbimage"> <span typeof="mw:File"><a href="https://en-m-wikipedia-org.translate.goog/wiki/File:Acceleration_vector_plane_polar_coords.svg?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-file-description"> <noscript> <img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Acceleration_vector_plane_polar_coords.svg/200px-Acceleration_vector_plane_polar_coords.svg.png" decoding="async" width="200" height="123" class="mw-file-element" data-file-width="326" data-file-height="201"> </noscript><span class="lazy-image-placeholder" style="width: 200px;height: 123px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Acceleration_vector_plane_polar_coords.svg/200px-Acceleration_vector_plane_polar_coords.svg.png" data-alt="" data-width="200" data-height="123" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/58/Acceleration_vector_plane_polar_coords.svg/300px-Acceleration_vector_plane_polar_coords.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/58/Acceleration_vector_plane_polar_coords.svg/400px-Acceleration_vector_plane_polar_coords.svg.png 2x" data-class="mw-file-element"> </span></a></span> </div> <div class="thumbcaption"> Acceleration vector <b>a</b>, not parallel to the radial motion but offset by the angular and Coriolis accelerations, nor tangent to the path but offset by the centripetal and radial accelerations. </div> </div> </div> <div class="trow" style="display:flex"> <div class="thumbcaption"> Kinematic vectors in plane <a href="https://en-m-wikipedia-org.translate.goog/wiki/Polar_coordinates?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Polar coordinates">polar coordinates</a>. Notice the setup is not restricted to 2d space, but may represent the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Osculating_plane?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Osculating plane">osculating plane</a> plane in a point of an arbitrary curve in any higher dimension. </div> </div> </div> </div> <p>In uniform <a href="https://en-m-wikipedia-org.translate.goog/wiki/Circular_motion?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Circular motion">circular motion</a>, that is moving with constant <i>speed</i> along a circular path, a particle experiences an acceleration resulting from the change of the direction of the velocity vector, while its magnitude remains constant. The derivative of the location of a point on a curve with respect to time, i.e. its velocity, turns out to be always exactly tangential to the curve, respectively orthogonal to the radius in this point. Since in uniform motion the velocity in the tangential direction does not change, the acceleration must be in radial direction, pointing to the center of the circle. This acceleration constantly changes the direction of the velocity to be tangent in the neighboring point, thereby rotating the velocity vector along the circle.</p> <ul> <li>For a given speed <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}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> v </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"> </noscript><span class="lazy-image-placeholder" style="width: 1.128ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" data-alt="{\displaystyle v}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, the magnitude of this geometrically caused acceleration (centripetal acceleration) is inversely proportional to the radius <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}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> r </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"> </noscript><span class="lazy-image-placeholder" style="width: 1.049ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" data-alt="{\displaystyle r}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> of the circle, and increases as the square of this speed: <span class="mwe-math-element" data-qid="Q2248131"><a href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Special:MathWikibase&qid=Q2248131&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" style="color:inherit;"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{c}={\frac {v^{2}}{r}}\,.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> c </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> r </mi> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{c}={\frac {v^{2}}{r}}\,.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5386ee595b15a9add6d43d21ac98fab8b12c27db" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.324ex; height:5.676ex;" alt="{\displaystyle a_{c}={\frac {v^{2}}{r}}\,.}"> </noscript><span class="lazy-image-placeholder" style="width: 9.324ex;height: 5.676ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5386ee595b15a9add6d43d21ac98fab8b12c27db" data-alt="{\displaystyle a_{c}={\frac {v^{2}}{r}}\,.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></a></span></li> <li>For a given <a href="https://en-m-wikipedia-org.translate.goog/wiki/Angular_velocity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Angular velocity">angular velocity</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 \omega }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω<!-- ω --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"> </noscript><span class="lazy-image-placeholder" style="width: 1.446ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" data-alt="{\displaystyle \omega }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, the centripetal acceleration is directly proportional to radius <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}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> r </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"> </noscript><span class="lazy-image-placeholder" style="width: 1.049ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" data-alt="{\displaystyle r}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>. This is due to the dependence of velocity <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}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> v </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"> </noscript><span class="lazy-image-placeholder" style="width: 1.128ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" data-alt="{\displaystyle v}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> on the radius <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}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> r </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"> </noscript><span class="lazy-image-placeholder" style="width: 1.049ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" data-alt="{\displaystyle r}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>. <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=\omega r.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> v </mi> <mo> = </mo> <mi> ω<!-- ω --> </mi> <mi> r </mi> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v=\omega r.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60ea3685a9b94b448033fd532fa489598f20a0bc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.367ex; height:1.676ex;" alt="{\displaystyle v=\omega r.}"> </noscript><span class="lazy-image-placeholder" style="width: 7.367ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60ea3685a9b94b448033fd532fa489598f20a0bc" data-alt="{\displaystyle v=\omega r.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span></li> </ul> <p>Expressing centripetal acceleration vector in polar components, where <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 \mathbf {r} }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {r} } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eca0f46511c4c986c48b254073732c0bd98ae0c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.102ex; height:1.676ex;" alt="{\displaystyle \mathbf {r} }"> </noscript><span class="lazy-image-placeholder" style="width: 1.102ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eca0f46511c4c986c48b254073732c0bd98ae0c1" data-alt="{\displaystyle \mathbf {r} }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> is a vector from the centre of the circle to the particle with magnitude equal to this distance, and considering the orientation of the acceleration towards the center, yields <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {a_{c}} =-{\frac {v^{2}}{|\mathbf {r} |}}\cdot {\frac {\mathbf {r} }{|\mathbf {r} |}}\,.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold"> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> c </mi> </mrow> </msub> </mrow> <mo> = </mo> <mo> −<!-- − --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ⋅<!-- ⋅ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> </mrow> </mfrac> </mrow> <mspace width="thinmathspace"></mspace> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {a_{c}} =-{\frac {v^{2}}{|\mathbf {r} |}}\cdot {\frac {\mathbf {r} }{|\mathbf {r} |}}\,.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0098c4881adc467b7c2805104758c4ea471c1b6d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.455ex; height:6.509ex;" alt="{\displaystyle \mathbf {a_{c}} =-{\frac {v^{2}}{|\mathbf {r} |}}\cdot {\frac {\mathbf {r} }{|\mathbf {r} |}}\,.}"> </noscript><span class="lazy-image-placeholder" style="width: 16.455ex;height: 6.509ex;vertical-align: -2.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0098c4881adc467b7c2805104758c4ea471c1b6d" data-alt="{\displaystyle \mathbf {a_{c}} =-{\frac {v^{2}}{|\mathbf {r} |}}\cdot {\frac {\mathbf {r} }{|\mathbf {r} |}}\,.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span></p> <p>As usual in rotations, the speed <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}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> v </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle v} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"> </noscript><span class="lazy-image-placeholder" style="width: 1.128ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" data-alt="{\displaystyle v}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> of a particle may be expressed as an <a href="https://en-m-wikipedia-org.translate.goog/wiki/Angular_velocity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Angular velocity"><i>angular speed</i></a> with respect to a point at the distance <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}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> r </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"> </noscript><span class="lazy-image-placeholder" style="width: 1.049ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" data-alt="{\displaystyle r}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> as <span class="mwe-math-element" data-qid="Q161635"><a href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Special:MathWikibase&qid=Q161635&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" style="color:inherit;"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega ={\frac {v}{r}}.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω<!-- ω --> </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi> v </mi> <mi> r </mi> </mfrac> </mrow> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega ={\frac {v}{r}}.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9ad55b7ffead5347a91fd9c0b4008946a13ee41" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.155ex; height:4.676ex;" alt="{\displaystyle \omega ={\frac {v}{r}}.}"> </noscript><span class="lazy-image-placeholder" style="width: 7.155ex;height: 4.676ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9ad55b7ffead5347a91fd9c0b4008946a13ee41" data-alt="{\displaystyle \omega ={\frac {v}{r}}.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></a></span></p> <p>Thus <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 \mathbf {a_{c}} =-\omega ^{2}\mathbf {r} \,.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="bold"> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> c </mi> </mrow> </msub> </mrow> <mo> = </mo> <mo> −<!-- − --> </mo> <msup> <mi> ω<!-- ω --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> r </mi> </mrow> <mspace width="thinmathspace"></mspace> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \mathbf {a_{c}} =-\omega ^{2}\mathbf {r} \,.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e04e2c9f9a5b24de7419347a42b60da7f99af078" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.914ex; height:3.009ex;" alt="{\displaystyle \mathbf {a_{c}} =-\omega ^{2}\mathbf {r} \,.}"> </noscript><span class="lazy-image-placeholder" style="width: 11.914ex;height: 3.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e04e2c9f9a5b24de7419347a42b60da7f99af078" data-alt="{\displaystyle \mathbf {a_{c}} =-\omega ^{2}\mathbf {r} \,.}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></p> <p>This acceleration and the mass of the particle determine the necessary <a href="https://en-m-wikipedia-org.translate.goog/wiki/Centripetal_force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Centripetal force">centripetal force</a>, directed <i>toward</i> the centre of the circle, as the net force acting on this particle to keep it in this uniform circular motion. The so-called '<a href="https://en-m-wikipedia-org.translate.goog/wiki/Centrifugal_force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Centrifugal force">centrifugal force</a>', appearing to act outward on the body, is a so-called <a href="https://en-m-wikipedia-org.translate.goog/wiki/Pseudo_force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Pseudo force">pseudo force</a> experienced in the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Frame_of_reference?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Frame of reference">frame of reference</a> of the body in circular motion, due to the body's <a href="https://en-m-wikipedia-org.translate.goog/wiki/Linear_momentum?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Linear momentum">linear momentum</a>, a vector tangent to the circle of motion.</p> <p>In a nonuniform circular motion, i.e., the speed along the curved path is changing, the acceleration has a non-zero component tangential to the curve, and is not confined to the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Principal_normal_vector?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Principal normal vector">principal normal</a>, which directs to the center of the osculating circle, that determines the radius <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}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> r </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"> </noscript><span class="lazy-image-placeholder" style="width: 1.049ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" data-alt="{\displaystyle r}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> for the centripetal acceleration. The tangential component is given by the angular acceleration <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 \alpha }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> α<!-- α --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \alpha } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"> </noscript><span class="lazy-image-placeholder" style="width: 1.488ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" data-alt="{\displaystyle \alpha }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, i.e., the rate of change <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 \alpha ={\dot {\omega }}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> α<!-- α --> </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi> ω<!-- ω --> </mi> <mo> ˙<!-- ˙ --> </mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \alpha ={\dot {\omega }}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5decfde4e2bbd6e948a608dd100f1939a3bfac30" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.032ex; height:2.176ex;" alt="{\displaystyle \alpha ={\dot {\omega }}}"> </noscript><span class="lazy-image-placeholder" style="width: 6.032ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5decfde4e2bbd6e948a608dd100f1939a3bfac30" data-alt="{\displaystyle \alpha ={\dot {\omega }}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> of the angular speed <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 \omega }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω<!-- ω --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"> </noscript><span class="lazy-image-placeholder" style="width: 1.446ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" data-alt="{\displaystyle \omega }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> times the radius <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}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> r </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"> </noscript><span class="lazy-image-placeholder" style="width: 1.049ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" data-alt="{\displaystyle r}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>. That is, <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{t}=r\alpha .}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> t </mi> </mrow> </msub> <mo> = </mo> <mi> r </mi> <mi> α<!-- α --> </mi> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{t}=r\alpha .} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/539041560190721697bf0e573f4854de5956e63e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.337ex; height:2.009ex;" alt="{\displaystyle a_{t}=r\alpha .}"> </noscript><span class="lazy-image-placeholder" style="width: 8.337ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/539041560190721697bf0e573f4854de5956e63e" data-alt="{\displaystyle a_{t}=r\alpha .}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span></p> <p>The sign of the tangential component of the acceleration is determined by the sign of the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Angular_acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Angular acceleration">angular acceleration</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 \alpha }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> α<!-- α --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \alpha } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"> </noscript><span class="lazy-image-placeholder" style="width: 1.488ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" data-alt="{\displaystyle \alpha }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>), and the tangent is always directed at right angles to the radius vector.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Coordinate_systems">Coordinate systems</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=10&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Coordinate systems" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-4 collapsible-block" id="mf-section-4"> <p>In multi-dimensional <a href="https://en-m-wikipedia-org.translate.goog/wiki/Cartesian_coordinate_system?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Cartesian coordinate system">Cartesian coordinate systems</a>, acceleration is broken up into components that correspond with each dimensional axis of the coordinate system. In a two-dimensional system, where there is an x-axis and a y-axis, corresponding acceleration components are defined as<sup id="cite_ref-12" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{x}=dv_{x}/dt=d^{2}x/dt^{2},}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> = </mo> <mi> d </mi> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo> / </mo> </mrow> <mi> d </mi> <mi> t </mi> <mo> = </mo> <msup> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> / </mo> </mrow> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> , </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{x}=dv_{x}/dt=d^{2}x/dt^{2},} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ce6e98d2757d56c5d422228c278534876e323b5" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.854ex; height:3.176ex;" alt="{\displaystyle a_{x}=dv_{x}/dt=d^{2}x/dt^{2},}"> </noscript><span class="lazy-image-placeholder" style="width: 23.854ex;height: 3.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ce6e98d2757d56c5d422228c278534876e323b5" data-alt="{\displaystyle a_{x}=dv_{x}/dt=d^{2}x/dt^{2},}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{y}=dv_{y}/dt=d^{2}y/dt^{2}.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo> = </mo> <mi> d </mi> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo> / </mo> </mrow> <mi> d </mi> <mi> t </mi> <mo> = </mo> <msup> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> y </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> / </mo> </mrow> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{y}=dv_{y}/dt=d^{2}y/dt^{2}.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2355d973a56142ddfe86d502c57d59fdf71bd7b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:23.434ex; height:3.343ex;" alt="{\displaystyle a_{y}=dv_{y}/dt=d^{2}y/dt^{2}.}"> </noscript><span class="lazy-image-placeholder" style="width: 23.434ex;height: 3.343ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2355d973a56142ddfe86d502c57d59fdf71bd7b" data-alt="{\displaystyle a_{y}=dv_{y}/dt=d^{2}y/dt^{2}.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span>The two-dimensional acceleration vector is then defined as <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 {\textbf {a}}=<a_{x},a_{y}>}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold"> a </mtext> </mrow> </mrow> <mo> =< </mo> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> , </mo> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo> > </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\textbf {a}}=<a_{x},a_{y}>} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd2e70de96488f95ef8f65e8c4a6a2d3b0bf739" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.375ex; height:2.509ex;" alt="{\displaystyle {\textbf {a}}=<a_{x},a_{y}>}"> </noscript><span class="lazy-image-placeholder" style="width: 14.375ex;height: 2.509ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd2e70de96488f95ef8f65e8c4a6a2d3b0bf739" data-alt="{\displaystyle {\textbf {a}}=<a_{x},a_{y}>}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>. The magnitude of this vector is found by the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Euclidean_distance?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Euclidean distance">distance formula</a> as<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |a|={\sqrt {a_{x}^{2}+a_{y}^{2}}}.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <msubsup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> </msqrt> </mrow> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle |a|={\sqrt {a_{x}^{2}+a_{y}^{2}}}.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d10cd937c68307c7f4e959db3ba68a6466b3f276" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.119ex; height:4.843ex;" alt="{\displaystyle |a|={\sqrt {a_{x}^{2}+a_{y}^{2}}}.}"> </noscript><span class="lazy-image-placeholder" style="width: 16.119ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d10cd937c68307c7f4e959db3ba68a6466b3f276" data-alt="{\displaystyle |a|={\sqrt {a_{x}^{2}+a_{y}^{2}}}.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span>In three-dimensional systems where there is an additional z-axis, the corresponding acceleration component is defined as<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{z}=dv_{z}/dt=d^{2}z/dt^{2}.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> z </mi> </mrow> </msub> <mo> = </mo> <mi> d </mi> <msub> <mi> v </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> z </mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo> / </mo> </mrow> <mi> d </mi> <mi> t </mi> <mo> = </mo> <msup> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> z </mi> <mrow class="MJX-TeXAtom-ORD"> <mo> / </mo> </mrow> <mi> d </mi> <msup> <mi> t </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a_{z}=dv_{z}/dt=d^{2}z/dt^{2}.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/beaf751a818ee39ea0bf50bf39a596399d27085c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.271ex; height:3.176ex;" alt="{\displaystyle a_{z}=dv_{z}/dt=d^{2}z/dt^{2}.}"> </noscript><span class="lazy-image-placeholder" style="width: 23.271ex;height: 3.176ex;vertical-align: -0.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/beaf751a818ee39ea0bf50bf39a596399d27085c" data-alt="{\displaystyle a_{z}=dv_{z}/dt=d^{2}z/dt^{2}.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span>The three-dimensional acceleration vector is defined as <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 {\textbf {a}}=<a_{x},a_{y},a_{z}>}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext mathvariant="bold"> a </mtext> </mrow> </mrow> <mo> =< </mo> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> , </mo> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo> , </mo> <msub> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> z </mi> </mrow> </msub> <mo> > </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\textbf {a}}=<a_{x},a_{y},a_{z}>} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f5c26e810aeeace73497545b45c5b6f7a7e4e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.64ex; height:2.509ex;" alt="{\displaystyle {\textbf {a}}=<a_{x},a_{y},a_{z}>}"> </noscript><span class="lazy-image-placeholder" style="width: 17.64ex;height: 2.509ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f5c26e810aeeace73497545b45c5b6f7a7e4e7" data-alt="{\displaystyle {\textbf {a}}=<a_{x},a_{y},a_{z}>}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> with its magnitude being determined by<span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"> <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |a|={\sqrt {a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}}.}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false"> | </mo> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <msubsup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <msubsup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> z </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> </msqrt> </mrow> <mo> . </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle |a|={\sqrt {a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}}.} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a499f6b42efa9cdb347ef5b7a225d236596b193" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.244ex; height:4.843ex;" alt="{\displaystyle |a|={\sqrt {a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}}.}"> </noscript><span class="lazy-image-placeholder" style="width: 21.244ex;height: 4.843ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a499f6b42efa9cdb347ef5b7a225d236596b193" data-alt="{\displaystyle |a|={\sqrt {a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}}.}" data-class="mwe-math-fallback-image-display mw-invert skin-invert"> </span></span></p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Relation_to_relativity">Relation to relativity</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=11&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Relation to relativity" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-5 collapsible-block" id="mf-section-5"> <div class="mw-heading mw-heading3"> <h3 id="Special_relativity">Special relativity</h3><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=12&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Special relativity" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"> <div role="note" class="hatnote navigation-not-searchable"> Main articles: <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special_relativity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special relativity">Special relativity</a> and <a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration_(special_relativity)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Acceleration (special relativity)">Acceleration (special relativity)</a> </div> <p>The special theory of relativity describes the behavior of objects traveling relative to other objects at speeds approaching that of light in vacuum. <a href="https://en-m-wikipedia-org.translate.goog/wiki/Newtonian_mechanics?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Newtonian mechanics">Newtonian mechanics</a> is exactly revealed to be an approximation to reality, valid to great accuracy at lower speeds. As the relevant speeds increase toward the speed of light, acceleration no longer follows classical equations.</p> <p>As speeds approach that of light, the acceleration produced by a given force decreases, becoming <a href="https://en-m-wikipedia-org.translate.goog/wiki/Infinitesimally?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Infinitesimally">infinitesimally</a> small as light speed is approached; an object with mass can approach this speed <a href="https://en-m-wikipedia-org.translate.goog/wiki/Asymptotically?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Asymptotically">asymptotically</a>, but never reach it.</p> <div class="mw-heading mw-heading3"> <h3 id="General_relativity">General relativity</h3><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=13&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: General relativity" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"> <div role="note" class="hatnote navigation-not-searchable"> Main article: <a href="https://en-m-wikipedia-org.translate.goog/wiki/General_relativity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="General relativity">General relativity</a> </div> <p>Unless the state of motion of an object is known, it is impossible to distinguish whether an observed force is due to <a href="https://en-m-wikipedia-org.translate.goog/wiki/Gravity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Gravity">gravity</a> or to acceleration—gravity and inertial acceleration have identical effects. <a href="https://en-m-wikipedia-org.translate.goog/wiki/Albert_Einstein?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Albert Einstein">Albert Einstein</a> called this the <a href="https://en-m-wikipedia-org.translate.goog/wiki/Equivalence_principle?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Equivalence principle">equivalence principle</a>, and said that only observers who feel no force at all—including the force of gravity—are justified in concluding that they are not accelerating.<sup id="cite_ref-Greene_13-0" class="reference"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_note-Greene-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Conversions">Conversions</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=14&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: Conversions" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-6 collapsible-block" id="mf-section-6"> <table class="wikitable" style="text-align:center"> <caption> <span class="nowrap">Conversions between common units of acceleration</span> </caption> <tbody> <tr> <th scope="col">Base value</th> <th scope="col">(<a href="https://en-m-wikipedia-org.translate.goog/wiki/Gal_(unit)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Gal (unit)">Gal</a>, or cm/s<sup>2</sup>)</th> <th scope="col">(<a href="https://en-m-wikipedia-org.translate.goog/wiki/Foot_per_second_squared?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Foot per second squared">ft/s<sup>2</sup></a>)</th> <th scope="col">(<a href="https://en-m-wikipedia-org.translate.goog/wiki/Metre_per_second_squared?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Metre per second squared">m/s<sup>2</sup></a>)</th> <th scope="col">(<a href="https://en-m-wikipedia-org.translate.goog/wiki/Standard_gravity?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Standard gravity">Standard gravity</a>, <i>g</i><sub>0</sub>)</th> </tr> <tr> <td>1 Gal, or cm/s<sup>2</sup></td> <td><b>1</b></td> <td><span class="nowrap"><span data-sort-value="6998328084000000000♠"></span>0.032<span style="margin-left:.25em;">8084</span></span></td> <td><span class="nowrap"><span data-sort-value="6998100000000000000♠"></span>0.01</span></td> <td><span class="nowrap"><span data-sort-value="6997101972000000000♠"></span>1.019<span style="margin-left:.25em;">72</span><span style="margin-left:0.25em;margin-right:0.15em;">×</span>10<sup>−3</sup></span></td> </tr> <tr> <td>1 ft/s<sup>2</sup></td> <td><span class="nowrap"><span data-sort-value="7001304800000000000♠"></span>30.4800</span></td> <td><b>1</b></td> <td><span class="nowrap"><span data-sort-value="6999304800000000000♠"></span>0.304<span style="margin-left:.25em;">800</span></span></td> <td><span class="nowrap"><span data-sort-value="6998310810000000000♠"></span>0.031<span style="margin-left:.25em;">0810</span></span></td> </tr> <tr> <td>1 m/s<sup>2</sup></td> <td><span class="nowrap"><span data-sort-value="7002100000000000000♠"></span>100</span></td> <td><span class="nowrap"><span data-sort-value="7000328084000000000♠"></span>3.280<span style="margin-left:.25em;">84</span></span></td> <td><b>1</b></td> <td><span class="nowrap"><span data-sort-value="6999101972000000000♠"></span>0.101<span style="margin-left:.25em;">972</span></span></td> </tr> <tr> <td>1 <i>g</i><sub>0</sub></td> <td><span class="nowrap"><span data-sort-value="7002980665000000000♠"></span>980.665</span></td> <td><span class="nowrap"><span data-sort-value="7001321740000000000♠"></span>32.1740</span></td> <td><span class="nowrap"><span data-sort-value="7000980665000000000♠"></span>9.806<span style="margin-left:.25em;">65</span></span></td> <td><b>1</b></td> </tr> </tbody> </table> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(7)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="See_also">See also</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=15&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: See also" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-7 collapsible-block" id="mf-section-7"> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style> <div class="div-col" style="column-width: 22em;"> <ul> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration_(differential_geometry)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Acceleration (differential geometry)">Acceleration (differential geometry)</a></li> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Four-vector?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Four-vector">Four-vector</a>: making the connection between space and time explicit</li> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Gravitational_acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Gravitational acceleration">Gravitational acceleration</a></li> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Inertia?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Inertia">Inertia</a></li> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Orders_of_magnitude_(acceleration)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Orders of magnitude (acceleration)">Orders of magnitude (acceleration)</a></li> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Shock_(mechanics)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Shock (mechanics)">Shock (mechanics)</a></li> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Shock_and_vibration_data_logger?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Shock and vibration data logger">Shock and vibration data logger</a><br> measuring 3-axis acceleration</li> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Space_travel_using_constant_acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="Space travel using constant acceleration">Space travel using constant acceleration</a></li> <li><a href="https://en-m-wikipedia-org.translate.goog/wiki/Specific_force?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Specific force">Specific force</a></li> </ul> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(8)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="References">References</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=16&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: References" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-8 collapsible-block" id="mf-section-8"> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style> <div class="reflist"> <div class="mw-references-wrap mw-references-columns"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBondi1980" class="citation book cs1">Bondi, Hermann (1980). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://archive.org/details/relativitycommon0000bond/page/3"><i>Relativity and Common Sense</i></a>. Courier Dover Publications. pp. <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://archive.org/details/relativitycommon0000bond/page/3">3</a>. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/978-0-486-24021-3?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/978-0-486-24021-3"><bdi>978-0-486-24021-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Relativity+and+Common+Sense&rft.pages=3&rft.pub=Courier+Dover+Publications&rft.date=1980&rft.isbn=978-0-486-24021-3&rft.aulast=Bondi&rft.aufirst=Hermann&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Frelativitycommon0000bond%2Fpage%2F3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-2">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLehrman1998" class="citation book cs1">Lehrman, Robert L. (1998). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://archive.org/details/physicseasyway00lehr_0/page/27"><i>Physics the Easy Way</i></a>. Barron's Educational Series. pp. <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://archive.org/details/physicseasyway00lehr_0/page/27">27</a>. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/978-0-7641-0236-3?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/978-0-7641-0236-3"><bdi>978-0-7641-0236-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+the+Easy+Way&rft.pages=27&rft.pub=Barron%27s+Educational+Series&rft.date=1998&rft.isbn=978-0-7641-0236-3&rft.aulast=Lehrman&rft.aufirst=Robert+L.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fphysicseasyway00lehr_0%2Fpage%2F27&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-3">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCrew2008" class="citation book cs1">Crew, Henry (2008). <i>The Principles of Mechanics</i>. BiblioBazaar, LLC. p. 43. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/978-0-559-36871-4?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/978-0-559-36871-4"><bdi>978-0-559-36871-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Principles+of+Mechanics&rft.pages=43&rft.pub=BiblioBazaar%2C+LLC&rft.date=2008&rft.isbn=978-0-559-36871-4&rft.aulast=Crew&rft.aufirst=Henry&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-4">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP._SmithR._C._Smith1991" class="citation book cs1">P. Smith; R. C. Smith (1991). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://books.google.com/books?id%3DZzh_unG7OAsC"><i>Mechanics</i></a> (2nd, illustrated, reprinted ed.). John Wiley & Sons. p. 39. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/978-0-471-92737-2?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/978-0-471-92737-2"><bdi>978-0-471-92737-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mechanics&rft.pages=39&rft.edition=2nd%2C+illustrated%2C+reprinted&rft.pub=John+Wiley+%26+Sons&rft.date=1991&rft.isbn=978-0-471-92737-2&rft.au=P.+Smith&rft.au=R.+C.+Smith&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DZzh_unG7OAsC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://books.google.com/books?id%3DZzh_unG7OAsC%26pg%3DPA39">Extract of page 39</a></span></li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-5">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohn_D._CutnellKenneth_W._Johnson2014" class="citation book cs1">John D. Cutnell; Kenneth W. Johnson (2014). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://books.google.com/books?id%3DPJWDBgAAQBAJ"><i>Physics, Volume One: Chapters 1-17, Volume 1</i></a> (1st0, illustrated ed.). John Wiley & Sons. p. 36. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/978-1-118-83688-0?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/978-1-118-83688-0"><bdi>978-1-118-83688-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics%2C+Volume+One%3A+Chapters+1-17%2C+Volume+1&rft.pages=36&rft.edition=1st0%2C+illustrated&rft.pub=John+Wiley+%26+Sons&rft.date=2014&rft.isbn=978-1-118-83688-0&rft.au=John+D.+Cutnell&rft.au=Kenneth+W.+Johnson&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPJWDBgAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://books.google.com/books?id%3DPJWDBgAAQBAJ%26pg%3DPA36">Extract of page 36</a></span></li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-6">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRaymond_A._SerwayChris_VuilleJerry_S._Faughn2008" class="citation book cs1">Raymond A. Serway; Chris Vuille; Jerry S. Faughn (2008). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://books.google.com/books?id%3DCX0u0mIOZ44C%26pg%3DPA32"><i>College Physics, Volume 10</i></a>. Cengage. p. 32. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/9780495386933?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/9780495386933"><bdi>9780495386933</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=College+Physics%2C+Volume+10&rft.pages=32&rft.pub=Cengage&rft.date=2008&rft.isbn=9780495386933&rft.au=Raymond+A.+Serway&rft.au=Chris+Vuille&rft.au=Jerry+S.+Faughn&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DCX0u0mIOZ44C%26pg%3DPA32&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-7">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1">Weisstein, Eric W. <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=http://mathworld.wolfram.com/ChainRule.html">"Chain Rule"</a>. <i>Wolfram MathWorld</i>. Wolfram Research<span class="reference-accessdate">. Retrieved <span class="nowrap">2 August</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Wolfram+MathWorld&rft.atitle=Chain+Rule&rft.aulast=Weisstein&rft.aufirst=Eric+W.&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FChainRule.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> <li id="cite_note-Andrews-8"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-Andrews_8-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLarry_C._AndrewsRonald_L._Phillips2003" class="citation book cs1">Larry C. Andrews; Ronald L. Phillips (2003). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://books.google.com/books?id%3DMwrDfvrQyWYC%26q%3Dparticle%2B%2522planar%2Bmotion%2522%26pg%3DPA164"><i>Mathematical Techniques for Engineers and Scientists</i></a>. SPIE Press. p. 164. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/978-0-8194-4506-3?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/978-0-8194-4506-3"><bdi>978-0-8194-4506-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Techniques+for+Engineers+and+Scientists&rft.pages=164&rft.pub=SPIE+Press&rft.date=2003&rft.isbn=978-0-8194-4506-3&rft.au=Larry+C.+Andrews&rft.au=Ronald+L.+Phillips&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DMwrDfvrQyWYC%26q%3Dparticle%2B%2522planar%2Bmotion%2522%26pg%3DPA164&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> <li id="cite_note-Chand-9"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-Chand_9-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCh_V_Ramana_MurthyNC_Srinivas2001" class="citation book cs1">Ch V Ramana Murthy; NC Srinivas (2001). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://books.google.com/books?id%3DQ0Pvv4vWOlQC%26pg%3DPA337"><i>Applied Mathematics</i></a>. New Delhi: S. Chand & Co. p. 337. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/978-81-219-2082-7?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/978-81-219-2082-7"><bdi>978-81-219-2082-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Applied+Mathematics&rft.place=New+Delhi&rft.pages=337&rft.pub=S.+Chand+%26+Co.&rft.date=2001&rft.isbn=978-81-219-2082-7&rft.au=Ch+V+Ramana+Murthy&rft.au=NC+Srinivas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DQ0Pvv4vWOlQC%26pg%3DPA337&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-10">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKeith_Johnson2001" class="citation book cs1">Keith Johnson (2001). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://books.google.com/books?id%3DD4nrQDzq1jkC%26q%3Dsuvat%26pg%3DPA135"><i>Physics for you: revised national curriculum edition for GCSE</i></a> (4th ed.). Nelson Thornes. p. 135. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/978-0-7487-6236-1?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/978-0-7487-6236-1"><bdi>978-0-7487-6236-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physics+for+you%3A+revised+national+curriculum+edition+for+GCSE&rft.pages=135&rft.edition=4th&rft.pub=Nelson+Thornes&rft.date=2001&rft.isbn=978-0-7487-6236-1&rft.au=Keith+Johnson&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DD4nrQDzq1jkC%26q%3Dsuvat%26pg%3DPA135&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-11">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavid_C._CassidyGerald_James_HoltonF._James_Rutherford2002" class="citation book cs1">David C. Cassidy; Gerald James Holton; F. James Rutherford (2002). <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://books.google.com/books?id%3DiPsKvL_ATygC%26q%3Dparabolic%2Barc%2Buniform-acceleration%2Bgalileo%26pg%3DPA146"><i>Understanding physics</i></a>. Birkhäuser. p. 146. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/978-0-387-98756-9?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/978-0-387-98756-9"><bdi>978-0-387-98756-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Understanding+physics&rft.pages=146&rft.pub=Birkh%C3%A4user&rft.date=2002&rft.isbn=978-0-387-98756-9&rft.au=David+C.+Cassidy&rft.au=Gerald+James+Holton&rft.au=F.+James+Rutherford&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DiPsKvL_ATygC%26q%3Dparabolic%2Barc%2Buniform-acceleration%2Bgalileo%26pg%3DPA146&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-12">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://www.feynmanlectures.caltech.edu/I_09.html">"The Feynman Lectures on Physics Vol. I Ch. 9: Newton's Laws of Dynamics"</a>. <i>www.feynmanlectures.caltech.edu</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-01-04</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.feynmanlectures.caltech.edu&rft.atitle=The+Feynman+Lectures+on+Physics+Vol.+I+Ch.+9%3A+Newton%E2%80%99s+Laws+of+Dynamics&rft_id=https%3A%2F%2Fwww.feynmanlectures.caltech.edu%2FI_09.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> <li id="cite_note-Greene-13"><span class="mw-cite-backlink"><b><a href="https://en-m-wikipedia-org.translate.goog/wiki/Acceleration?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja#cite_ref-Greene_13-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreene" class="citation book cs1"><a href="https://en-m-wikipedia-org.translate.goog/wiki/Brian_Greene?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Brian Greene">Greene, Brian</a>. <a href="https://en-m-wikipedia-org.translate.goog/wiki/The_Fabric_of_the_Cosmos?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="The Fabric of the Cosmos"><i>The Fabric of the Cosmos: Space, Time, and the Texture of Reality</i></a>. Vintage. p. 67. <a href="https://en-m-wikipedia-org.translate.goog/wiki/ISBN_(identifier)?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="https://en-m-wikipedia-org.translate.goog/wiki/Special:BookSources/0-375-72720-5?_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Special:BookSources/0-375-72720-5"><bdi>0-375-72720-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Fabric+of+the+Cosmos%3A+Space%2C+Time%2C+and+the+Texture+of+Reality&rft.pages=67&rft.pub=Vintage&rft.isbn=0-375-72720-5&rft.aulast=Greene&rft.aufirst=Brian&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAcceleration" class="Z3988"></span></span></li> </ol> </div> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(9)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="External_links">External links</h2><span class="mw-editsection"> <a role="button" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=edit&section=17&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja" title="Edit section: External links" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>edit</span> </a> </span> </div> <section class="mf-section-9 collapsible-block" id="mf-section-9"> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style> <style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style> <div class="side-box side-box-right plainlinks sistersitebox"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"> <span class="noviewer" typeof="mw:File"><span> <noscript> <img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" data-file-width="1024" data-file-height="1376"> </noscript><span class="lazy-image-placeholder" style="width: 30px;height: 40px;" data-src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" data-alt="" data-width="30" data-height="40" data-srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-class="mw-file-element"> </span></span></span> </div> <div class="side-box-text plainlist"> Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://commons.wikimedia.org/wiki/Category:Acceleration" class="extiw" title="commons:Category:Acceleration">Acceleration</a></span>. </div> </div> </div> <ul> <li><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=http://www.unitjuggler.com/convert-acceleration-from-ms2-to-fts2.html">Acceleration Calculator</a> Simple acceleration unit converter</li> <li><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://www.easyunitconverter.com/acceleration-calculator">Acceleration Calculator</a> Acceleration Conversion calculator converts units form meter per second square, kilometre per second square, millimeter per second square & more with metric conversion.</li> </ul> <div class="navbox-styles"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style> </div> <div class="navbox-styles"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"> </div> <div class="navbox-styles"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"> <style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1038841319"> </div><!-- NewPP limit report Parsed by mw‐web.codfw.main‐f69cdc8f6‐rt2p2 Cached time: 20241122140328 Cache expiry: 2592000 Reduced expiry: false Complications: [vary‐revision‐sha1, show‐toc] CPU time usage: 0.860 seconds Real time usage: 1.156 seconds Preprocessor visited node count: 6162/1000000 Post‐expand include size: 120501/2097152 bytes Template argument size: 10981/2097152 bytes Highest expansion depth: 14/100 Expensive parser function count: 12/500 Unstrip recursion depth: 1/20 Unstrip post‐expand size: 118917/5000000 bytes Lua time usage: 0.443/10.000 seconds Lua memory usage: 10271536/52428800 bytes Number of Wikibase entities loaded: 1/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 862.299 1 -total 18.45% 159.121 1 Template:Reflist 17.98% 155.012 1 Template:Classical_mechanics 17.72% 152.778 1 Template:Sidebar_with_collapsible_lists 15.09% 130.126 11 Template:Cite_book 10.86% 93.654 2 Template:Navbox 9.30% 80.236 77 Template:Math 9.28% 80.047 1 Template:Short_description 8.06% 69.515 1 Template:Commons_category 8.03% 69.264 1 Template:Classical_mechanics_derived_SI_units --> <!-- Saved in parser cache with key enwiki:pcache:idhash:2443-0!canonical and timestamp 20241122140328 and revision id 1249934770. Rendering was triggered because: page-view --> </section> </div><!-- MobileFormatter took 0.035 seconds --><!--esi <esi:include src="/esitest-fa8a495983347898/content" /> --> <noscript> <img src="https://login.m.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&mobile=1" alt="" width="1" height="1" style="border: none; position: absolute;"> </noscript> <div class="printfooter" data-nosnippet=""> Retrieved from "<a dir="ltr" href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://en.wikipedia.org/w/index.php?title%3DAcceleration%26oldid%3D1249934770">https://en.wikipedia.org/w/index.php?title=Acceleration&oldid=1249934770</a>" </div> </div> </div> <div class="post-content" id="page-secondary-actions"> </div> </main> <footer class="mw-footer minerva-footer" role="contentinfo"><a class="last-modified-bar" href="https://en-m-wikipedia-org.translate.goog/w/index.php?title=Acceleration&action=history&_x_tr_sl=en&_x_tr_tl=ja&_x_tr_hl=ja"> <div class="post-content 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class="interlanguage-link-target"><span>Afrikaans</span></a></li> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://als.wikipedia.org/wiki/Beschleunigung" title="Beschleunigung – Alemannic" lang="gsw" hreflang="gsw" data-title="Beschleunigung" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://am.wikipedia.org/wiki/%25E1%258D%258D%25E1%258C%25A5%25E1%258A%2595%25E1%258C%25A5%25E1%258A%2590%25E1%2589%25B5" title="ፍጥንጥነት – Amharic" lang="am" hreflang="am" data-title="ፍጥንጥነት" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li> <li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://anp.wikipedia.org/wiki/%25E0%25A4%25A4%25E0%25A5%258D%25E0%25A4%25B5%25E0%25A4%25B0%25E0%25A4%25A3" title="त्वरण – Angika" lang="anp" hreflang="anp" data-title="त्वरण" 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://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ar.wikipedia.org/wiki/%25D8%25AA%25D8%25B3%25D8%25A7%25D8%25B1%25D8%25B9" title="تسارع – Arabic" lang="ar" hreflang="ar" data-title="تسارع" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li> <li class="interlanguage-link interwiki-an mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://an.wikipedia.org/wiki/Aceleraci%25C3%25B3n" title="Aceleración – Aragonese" lang="an" hreflang="an" data-title="Aceleración" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li> <li class="interlanguage-link interwiki-as mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://as.wikipedia.org/wiki/%25E0%25A6%25A4%25E0%25A7%258D%25E0%25A6%25AC%25E0%25A7%25B0%25E0%25A6%25A3" title="ত্বৰণ – Assamese" lang="as" hreflang="as" data-title="ত্বৰণ" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li> <li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ast.wikipedia.org/wiki/Aceleraci%25C3%25B3n" title="Aceleración – Asturian" lang="ast" hreflang="ast" data-title="Aceleración" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li> <li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://gn.wikipedia.org/wiki/%25C3%2591emoag%25CC%2583e" title="Ñemoag̃e – Guarani" lang="gn" hreflang="gn" data-title="Ñemoag̃e" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li> <li class="interlanguage-link interwiki-az mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://az.wikipedia.org/wiki/T%25C9%2599cil" title="Təcil – Azerbaijani" lang="az" hreflang="az" data-title="Təcil" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li> <li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://azb.wikipedia.org/wiki/%25D8%25A7%25DB%258C%25D9%2588%25D9%2585%25D9%2587" title="ایومه – South Azerbaijani" lang="azb" hreflang="azb" data-title="ایومه" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li> <li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://bn.wikipedia.org/wiki/%25E0%25A6%25A4%25E0%25A7%258D%25E0%25A6%25AC%25E0%25A6%25B0%25E0%25A6%25A3" title="ত্বরণ – Bangla" lang="bn" hreflang="bn" data-title="ত্বরণ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li> <li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://zh-min-nan.wikipedia.org/wiki/Ka-sok-t%25C5%258D%25CD%2598" title="Ka-sok-tō͘ – Minnan" lang="nan" hreflang="nan" data-title="Ka-sok-tō͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li> <li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ba.wikipedia.org/wiki/%25D0%25A2%25D0%25B8%25D2%2599%25D0%25BB%25D3%2599%25D0%25BD%25D0%25B5%25D1%2588" title="Тиҙләнеш – Bashkir" lang="ba" hreflang="ba" data-title="Тиҙләнеш" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li> <li class="interlanguage-link interwiki-be mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://be.wikipedia.org/wiki/%25D0%259F%25D0%25B0%25D1%2581%25D0%25BA%25D0%25B0%25D1%2580%25D1%258D%25D0%25BD%25D0%25BD%25D0%25B5" title="Паскарэнне – Belarusian" lang="be" hreflang="be" data-title="Паскарэнне" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li> <li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://be-tarask.wikipedia.org/wiki/%25D0%259F%25D0%25B0%25D1%2581%25D0%25BA%25D0%25B0%25D1%2580%25D1%258D%25D0%25BD%25D1%258C%25D0%25BD%25D0%25B5" title="Паскарэньне – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Паскарэньне" 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-bh mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://bh.wikipedia.org/wiki/%25E0%25A4%25AA%25E0%25A4%25B0%25E0%25A4%25B5%25E0%25A5%2587%25E0%25A4%2597" title="परवेग – Bhojpuri" lang="bh" hreflang="bh" data-title="परवेग" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li> <li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://bcl.wikipedia.org/wiki/Akselerasyon" title="Akselerasyon – Central Bikol" lang="bcl" hreflang="bcl" data-title="Akselerasyon" 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-bg mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://bg.wikipedia.org/wiki/%25D0%25A3%25D1%2581%25D0%25BA%25D0%25BE%25D1%2580%25D0%25B5%25D0%25BD%25D0%25B8%25D0%25B5" title="Ускорение – Bulgarian" lang="bg" hreflang="bg" data-title="Ускорение" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li> <li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://bo.wikipedia.org/wiki/%25E0%25BD%2598%25E0%25BE%25B1%25E0%25BD%25B4%25E0%25BD%25A2%25E0%25BC%258B%25E0%25BD%25A6%25E0%25BE%25A3%25E0%25BD%25BC%25E0%25BD%2593%25E0%25BC%258D" title="མྱུར་སྣོན། – Tibetan" lang="bo" hreflang="bo" data-title="མྱུར་སྣོན།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetan" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li> <li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://bs.wikipedia.org/wiki/Ubrzanje" title="Ubrzanje – Bosnian" lang="bs" hreflang="bs" data-title="Ubrzanje" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li> <li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://bxr.wikipedia.org/wiki/%25D0%25A5%25D1%2583%25D1%2580%25D0%25B4%25D0%25B0%25D0%25B4%25D1%2585%25D0%25B0%25D0%25BB" title="Хурдадхал – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Хурдадхал" 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://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ca.wikipedia.org/wiki/Acceleraci%25C3%25B3" title="Acceleració – Catalan" lang="ca" hreflang="ca" data-title="Acceleració" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li> <li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://cv.wikipedia.org/wiki/%25D0%25A5%25C4%2583%25D0%25B2%25C4%2583%25D1%2580%25D1%2582%25D0%25BB%25D0%25B0%25D0%25BD%25D1%2583" title="Хăвăртлану – Chuvash" lang="cv" hreflang="cv" data-title="Хăвăртлану" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li> <li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://cs.wikipedia.org/wiki/Zrychlen%25C3%25AD" title="Zrychlení – Czech" lang="cs" hreflang="cs" data-title="Zrychlení" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li> <li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://sn.wikipedia.org/wiki/Rufangu" title="Rufangu – Shona" lang="sn" hreflang="sn" data-title="Rufangu" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li> <li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://cy.wikipedia.org/wiki/Cyflymiad" title="Cyflymiad – Welsh" lang="cy" hreflang="cy" data-title="Cyflymiad" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li> <li class="interlanguage-link interwiki-da mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://da.wikipedia.org/wiki/Acceleration" title="Acceleration – Danish" lang="da" hreflang="da" data-title="Acceleration" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li> <li class="interlanguage-link interwiki-de mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://de.wikipedia.org/wiki/Beschleunigung" title="Beschleunigung – German" lang="de" hreflang="de" data-title="Beschleunigung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li> <li class="interlanguage-link interwiki-et mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://et.wikipedia.org/wiki/Kiirendus" title="Kiirendus – Estonian" lang="et" hreflang="et" data-title="Kiirendus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li> <li class="interlanguage-link interwiki-el mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://el.wikipedia.org/wiki/%25CE%2595%25CF%2580%25CE%25B9%25CF%2584%25CE%25AC%25CF%2587%25CF%2585%25CE%25BD%25CF%2583%25CE%25B7" title="Επιτάχυνση – Greek" lang="el" hreflang="el" data-title="Επιτάχυνση" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li> <li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://eml.wikipedia.org/wiki/Azelerazi%25C3%25A5n" title="Azeleraziån – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Azeleraziån" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li> <li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://myv.wikipedia.org/wiki/%25D0%259A%25D0%25B0%25D0%25BF%25D1%2588%25D0%25B0%25D0%25B2%25D1%2582%25D0%25BE%25D0%25BC%25D0%25B0" title="Капшавтома – Erzya" lang="myv" hreflang="myv" data-title="Капшавтома" data-language-autonym="Эрзянь" data-language-local-name="Erzya" class="interlanguage-link-target"><span>Эрзянь</span></a></li> <li class="interlanguage-link interwiki-es mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://es.wikipedia.org/wiki/Aceleraci%25C3%25B3n" title="Aceleración – Spanish" lang="es" hreflang="es" data-title="Aceleración" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li> <li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://eo.wikipedia.org/wiki/Akcelo" title="Akcelo – Esperanto" lang="eo" hreflang="eo" data-title="Akcelo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li> <li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://eu.wikipedia.org/wiki/Azelerazio" title="Azelerazio – Basque" lang="eu" hreflang="eu" data-title="Azelerazio" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li> <li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://fa.wikipedia.org/wiki/%25D8%25B4%25D8%25AA%25D8%25A7%25D8%25A8" title="شتاب – Persian" lang="fa" hreflang="fa" data-title="شتاب" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li> <li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://hif.wikipedia.org/wiki/Acceleration" title="Acceleration – Fiji Hindi" lang="hif" hreflang="hif" data-title="Acceleration" 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-fr mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://fr.wikipedia.org/wiki/Acc%25C3%25A9l%25C3%25A9ration" title="Accélération – French" lang="fr" hreflang="fr" data-title="Accélération" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li> <li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://fy.wikipedia.org/wiki/Fersnelling_(natuerkunde)" title="Fersnelling (natuerkunde) – Western Frisian" lang="fy" hreflang="fy" data-title="Fersnelling (natuerkunde)" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target"><span>Frysk</span></a></li> <li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ga.wikipedia.org/wiki/Luasgh%25C3%25A9ar%25C3%25BA" title="Luasghéarú – Irish" lang="ga" hreflang="ga" data-title="Luasghéarú" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li> <li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://gv.wikipedia.org/wiki/Siyraghey" title="Siyraghey – Manx" lang="gv" hreflang="gv" data-title="Siyraghey" data-language-autonym="Gaelg" data-language-local-name="Manx" class="interlanguage-link-target"><span>Gaelg</span></a></li> <li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://gl.wikipedia.org/wiki/Aceleraci%25C3%25B3n" title="Aceleración – Galician" lang="gl" hreflang="gl" data-title="Aceleración" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li> <li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://hak.wikipedia.org/wiki/K%25C3%25A2-suk-thu" title="Kâ-suk-thu – Hakka Chinese" lang="hak" hreflang="hak" data-title="Kâ-suk-thu" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li> <li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ko.wikipedia.org/wiki/%25EA%25B0%2580%25EC%2586%258D%25EB%258F%2584" title="가속도 – Korean" lang="ko" hreflang="ko" data-title="가속도" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li> <li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://hy.wikipedia.org/wiki/%25D4%25B1%25D6%2580%25D5%25A1%25D5%25A3%25D5%25A1%25D6%2581%25D5%25B8%25D6%2582%25D5%25B4" title="Արագացում – Armenian" lang="hy" hreflang="hy" data-title="Արագացում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li> <li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://hi.wikipedia.org/wiki/%25E0%25A4%25A4%25E0%25A5%258D%25E0%25A4%25B5%25E0%25A4%25B0%25E0%25A4%25A3" title="त्वरण – Hindi" lang="hi" hreflang="hi" data-title="त्वरण" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li> <li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://hr.wikipedia.org/wiki/Ubrzanje" title="Ubrzanje – Croatian" lang="hr" hreflang="hr" data-title="Ubrzanje" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li> <li class="interlanguage-link interwiki-io mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://io.wikipedia.org/wiki/Acelero" title="Acelero – Ido" lang="io" hreflang="io" data-title="Acelero" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li> <li class="interlanguage-link interwiki-bpy mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://bpy.wikipedia.org/wiki/%25E0%25A6%25A4%25E0%25A7%258D%25E0%25A6%25AC%25E0%25A6%25B0%25E0%25A6%25A3" title="ত্বরণ – Bishnupriya" lang="bpy" hreflang="bpy" data-title="ত্বরণ" data-language-autonym="বিষ্ণুপ্রিয়া মণিপুরী" data-language-local-name="Bishnupriya" class="interlanguage-link-target"><span>বিষ্ণুপ্রিয়া মণিপুরী</span></a></li> <li class="interlanguage-link interwiki-id mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://id.wikipedia.org/wiki/Percepatan" title="Percepatan – Indonesian" lang="id" hreflang="id" data-title="Percepatan" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li> <li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ia.wikipedia.org/wiki/Acceleration" title="Acceleration – Interlingua" lang="ia" hreflang="ia" data-title="Acceleration" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li> <li class="interlanguage-link interwiki-is mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://is.wikipedia.org/wiki/Hr%25C3%25B6%25C3%25B0un" title="Hröðun – Icelandic" lang="is" hreflang="is" data-title="Hröðun" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li> <li class="interlanguage-link interwiki-it mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://it.wikipedia.org/wiki/Accelerazione" title="Accelerazione – Italian" lang="it" hreflang="it" data-title="Accelerazione" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li> <li class="interlanguage-link interwiki-he mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://he.wikipedia.org/wiki/%25D7%25AA%25D7%2590%25D7%2595%25D7%25A6%25D7%2594" title="תאוצה – Hebrew" lang="he" hreflang="he" data-title="תאוצה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li> <li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://kbp.wikipedia.org/wiki/Ki%25C9%2596i_ki%25C9%2596i_wonuu_(acc%25C3%25A9l%25C3%25A9ration)" title="Kiɖi kiɖi wonuu (accélération) – Kabiye" lang="kbp" hreflang="kbp" data-title="Kiɖi kiɖi wonuu (accélération)" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li> <li class="interlanguage-link interwiki-krc badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://krc.wikipedia.org/wiki/%25D0%25A2%25D0%25B5%25D1%2580%25D0%25BA%25D0%25BB%25D0%25B5%25D0%25BD%25D0%25B8%25D1%2583" title="Терклениу – Karachay-Balkar" lang="krc" hreflang="krc" data-title="Терклениу" data-language-autonym="Къарачай-малкъар" data-language-local-name="Karachay-Balkar" class="interlanguage-link-target"><span>Къарачай-малкъар</span></a></li> <li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ka.wikipedia.org/wiki/%25E1%2583%2590%25E1%2583%25A9%25E1%2583%25A5%25E1%2583%2590%25E1%2583%25A0%25E1%2583%2594%25E1%2583%2591%25E1%2583%2590" title="აჩქარება – Georgian" lang="ka" hreflang="ka" data-title="აჩქარება" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li> <li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://kk.wikipedia.org/wiki/%25D2%25AE%25D0%25B4%25D0%25B5%25D1%2583" title="Үдеу – Kazakh" lang="kk" hreflang="kk" data-title="Үдеу" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li> <li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://kw.wikipedia.org/wiki/Uskisheans" title="Uskisheans – Cornish" lang="kw" hreflang="kw" data-title="Uskisheans" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target"><span>Kernowek</span></a></li> <li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://sw.wikipedia.org/wiki/Mchapuko" title="Mchapuko – Swahili" lang="sw" hreflang="sw" data-title="Mchapuko" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li> <li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ht.wikipedia.org/wiki/Akselerasyon_santrip%25C3%25A8d" title="Akselerasyon santripèd – Haitian Creole" lang="ht" hreflang="ht" data-title="Akselerasyon santripèd" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li> <li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ku.wikipedia.org/wiki/Lezdan_(fiz%25C3%25AEk)" title="Lezdan (fizîk) – Kurdish" lang="ku" hreflang="ku" data-title="Lezdan (fizîk)" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li> <li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ky.wikipedia.org/wiki/%25D0%25AB%25D0%25BB%25D0%25B4%25D0%25B0%25D0%25BC%25D0%25B4%25D0%25B0%25D0%25BD%25D1%2583%25D1%2583" title="Ылдамдануу – Kyrgyz" lang="ky" hreflang="ky" data-title="Ылдамдануу" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li> <li class="interlanguage-link interwiki-la mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://la.wikipedia.org/wiki/Acceleratio" title="Acceleratio – Latin" lang="la" hreflang="la" data-title="Acceleratio" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li> <li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://lv.wikipedia.org/wiki/Pa%25C4%2581trin%25C4%2581jums" title="Paātrinājums – Latvian" lang="lv" hreflang="lv" data-title="Paātrinājums" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li> <li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://lt.wikipedia.org/wiki/Pagreitis" title="Pagreitis – Lithuanian" lang="lt" hreflang="lt" data-title="Pagreitis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li> <li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://lfn.wikipedia.org/wiki/Aselera" title="Aselera – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Aselera" 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-lmo mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://lmo.wikipedia.org/wiki/Acelerazion" title="Acelerazion – Lombard" lang="lmo" hreflang="lmo" data-title="Acelerazion" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li> <li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://hu.wikipedia.org/wiki/Gyorsul%25C3%25A1s" title="Gyorsulás – Hungarian" lang="hu" hreflang="hu" data-title="Gyorsulás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li> <li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://mk.wikipedia.org/wiki/%25D0%2597%25D0%25B0%25D0%25B1%25D1%2580%25D0%25B7%25D1%2583%25D0%25B2%25D0%25B0%25D1%259A%25D0%25B5" title="Забрзување – Macedonian" lang="mk" hreflang="mk" data-title="Забрзување" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li> <li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ml.wikipedia.org/wiki/%25E0%25B4%25A4%25E0%25B5%258D%25E0%25B4%25B5%25E0%25B4%25B0%25E0%25B4%25A3%25E0%25B4%2582" title="ത്വരണം – Malayalam" lang="ml" hreflang="ml" data-title="ത്വരണം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li> <li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://mr.wikipedia.org/wiki/%25E0%25A4%25AA%25E0%25A5%258D%25E0%25A4%25B0%25E0%25A4%25B5%25E0%25A5%2587%25E0%25A4%2597" title="प्रवेग – Marathi" lang="mr" hreflang="mr" data-title="प्रवेग" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li> <li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://arz.wikipedia.org/wiki/%25D8%25AA%25D8%25B3%25D8%25B1%25D9%258A%25D8%25B9" title="تسريع – Egyptian Arabic" lang="arz" hreflang="arz" data-title="تسريع" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li> <li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ms.wikipedia.org/wiki/Pecutan" title="Pecutan – Malay" lang="ms" hreflang="ms" data-title="Pecutan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li> <li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://cdo.wikipedia.org/wiki/G%25C4%2583-s%25C3%25B3k-d%25C3%25B4" title="Gă-sók-dô – Mindong" lang="cdo" hreflang="cdo" data-title="Gă-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-mn mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://mn.wikipedia.org/wiki/%25D0%25A5%25D1%2583%25D1%2580%25D0%25B4%25D0%25B0%25D1%2582%25D0%25B3%25D0%25B0%25D0%25BB" title="Хурдатгал – Mongolian" lang="mn" hreflang="mn" data-title="Хурдатгал" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li> <li class="interlanguage-link interwiki-my mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://my.wikipedia.org/wiki/%25E1%2580%25A1%25E1%2580%259C%25E1%2580%25BB%25E1%2580%2584%25E1%2580%25BA%25E1%2580%2595%25E1%2580%25BC%25E1%2580%25B1%25E1%2580%25AC%25E1%2580%2584%25E1%2580%25BA%25E1%2580%25B8%25E1%2580%2594%25E1%2580%25BE%25E1%2580%25AF%25E1%2580%2594%25E1%2580%25BA%25E1%2580%25B8" title="အလျင်ပြောင်းနှုန်း – Burmese" lang="my" hreflang="my" data-title="အလျင်ပြောင်းနှုန်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li> <li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://nl.wikipedia.org/wiki/Versnelling_(natuurkunde)" title="Versnelling (natuurkunde) – Dutch" lang="nl" hreflang="nl" data-title="Versnelling (natuurkunde)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li> <li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ne.wikipedia.org/wiki/%25E0%25A4%25AA%25E0%25A5%258D%25E0%25A4%25B0%25E0%25A4%25B5%25E0%25A5%2587%25E0%25A4%2597" title="प्रवेग – Nepali" lang="ne" hreflang="ne" data-title="प्रवेग" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li> <li class="interlanguage-link interwiki-new mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://new.wikipedia.org/wiki/%25E0%25A4%25AA%25E0%25A5%258D%25E0%25A4%25B0%25E0%25A4%25B5%25E0%25A5%2587%25E0%25A4%2597" title="प्रवेग – Newari" lang="new" hreflang="new" data-title="प्रवेग" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li> <li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ja.wikipedia.org/wiki/%25E5%258A%25A0%25E9%2580%259F%25E5%25BA%25A6" title="加速度 – Japanese" lang="ja" hreflang="ja" data-title="加速度" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li> <li class="interlanguage-link interwiki-nap mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://nap.wikipedia.org/wiki/Accellerazione" title="Accellerazione – Neapolitan" lang="nap" hreflang="nap" data-title="Accellerazione" data-language-autonym="Napulitano" data-language-local-name="Neapolitan" class="interlanguage-link-target"><span>Napulitano</span></a></li> <li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://frr.wikipedia.org/wiki/Faardferanrang" title="Faardferanrang – Northern Frisian" lang="frr" hreflang="frr" data-title="Faardferanrang" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li> <li class="interlanguage-link interwiki-no mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://no.wikipedia.org/wiki/Akselerasjon" title="Akselerasjon – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Akselerasjon" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://nn.wikipedia.org/wiki/Akselerasjon" title="Akselerasjon – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Akselerasjon" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li> <li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://nov.wikipedia.org/wiki/Akseleratione" title="Akseleratione – Novial" lang="nov" hreflang="nov" data-title="Akseleratione" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li> <li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://oc.wikipedia.org/wiki/Acceleracion" title="Acceleracion – Occitan" lang="oc" hreflang="oc" data-title="Acceleracion" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li> <li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://uz.wikipedia.org/wiki/Tezlanish" title="Tezlanish – Uzbek" lang="uz" hreflang="uz" data-title="Tezlanish" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li> <li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://pa.wikipedia.org/wiki/%25E0%25A8%25AA%25E0%25A9%258D%25E0%25A8%25B0%25E0%25A8%25B5%25E0%25A9%2587%25E0%25A8%2597" title="ਪ੍ਰਵੇਗ – Punjabi" lang="pa" hreflang="pa" data-title="ਪ੍ਰਵੇਗ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li> <li class="interlanguage-link interwiki-pag mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://pag.wikipedia.org/wiki/Akpelusyon" title="Akpelusyon – Pangasinan" lang="pag" hreflang="pag" data-title="Akpelusyon" data-language-autonym="Pangasinan" data-language-local-name="Pangasinan" class="interlanguage-link-target"><span>Pangasinan</span></a></li> <li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://pnb.wikipedia.org/wiki/%25D8%25A7%25D8%25B3%25D8%25B1%25D8%25A7%25D8%25B9" title="اسراع – Western Punjabi" lang="pnb" hreflang="pnb" data-title="اسراع" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li> <li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ps.wikipedia.org/wiki/%25D8%25B3%25D8%25B1%25D8%25B9%25D8%25AA" title="سرعت – Pashto" lang="ps" hreflang="ps" data-title="سرعت" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li> <li class="interlanguage-link interwiki-km mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://km.wikipedia.org/wiki/%25E1%259E%259F%25E1%259F%2586%25E1%259E%2591%25E1%259E%25BB%25E1%259F%2587" title="សំទុះ – Khmer" lang="km" hreflang="km" data-title="សំទុះ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li> <li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://pms.wikipedia.org/wiki/Acelerassion" title="Acelerassion – Piedmontese" lang="pms" hreflang="pms" data-title="Acelerassion" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li> <li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://nds.wikipedia.org/wiki/Versnellen" title="Versnellen – Low German" lang="nds" hreflang="nds" data-title="Versnellen" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li> <li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://pl.wikipedia.org/wiki/Przyspieszenie" title="Przyspieszenie – Polish" lang="pl" hreflang="pl" data-title="Przyspieszenie" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li> <li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://pt.wikipedia.org/wiki/Acelera%25C3%25A7%25C3%25A3o" title="Aceleração – Portuguese" lang="pt" hreflang="pt" data-title="Aceleração" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li> <li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ro.wikipedia.org/wiki/Accelera%25C8%259Bie" title="Accelerație – Romanian" lang="ro" hreflang="ro" data-title="Accelerație" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li> <li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://qu.wikipedia.org/wiki/P%2527ikwachiy" title="P'ikwachiy – Quechua" lang="qu" hreflang="qu" data-title="P'ikwachiy" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li> <li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://rue.wikipedia.org/wiki/%25D0%2590%25D0%25BA%25D1%2586%25D0%25B5%25D0%25BB%25D0%25B5%25D1%2580%25D0%25B0%25D1%2586%25D1%2596%25D1%258F" title="Акцелерація – Rusyn" lang="rue" hreflang="rue" data-title="Акцелерація" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li> <li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ru.wikipedia.org/wiki/%25D0%25A3%25D1%2581%25D0%25BA%25D0%25BE%25D1%2580%25D0%25B5%25D0%25BD%25D0%25B8%25D0%25B5" title="Ускорение – Russian" lang="ru" hreflang="ru" data-title="Ускорение" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li> <li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://sc.wikipedia.org/wiki/Atzellerada" title="Atzellerada – Sardinian" lang="sc" hreflang="sc" data-title="Atzellerada" data-language-autonym="Sardu" data-language-local-name="Sardinian" class="interlanguage-link-target"><span>Sardu</span></a></li> <li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://sq.wikipedia.org/wiki/Nxitimi" title="Nxitimi – Albanian" lang="sq" hreflang="sq" data-title="Nxitimi" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li> <li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://scn.wikipedia.org/wiki/Accilirazzioni" title="Accilirazzioni – Sicilian" lang="scn" hreflang="scn" data-title="Accilirazzioni" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li> <li class="interlanguage-link interwiki-si mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://si.wikipedia.org/wiki/%25E0%25B6%25AD%25E0%25B7%258A%25E0%25B7%2580%25E0%25B6%25BB%25E0%25B6%25AB%25E0%25B6%25BA" title="ත්වරණය – Sinhala" lang="si" hreflang="si" data-title="ත්වරණය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li> <li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://simple.wikipedia.org/wiki/Acceleration" title="Acceleration – Simple English" lang="en-simple" hreflang="en-simple" data-title="Acceleration" 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-sd mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://sd.wikipedia.org/wiki/%25D8%25A7%25D8%25B3%25D8%25B1%25D8%25A7%25D8%25B9" title="اسراع – Sindhi" lang="sd" hreflang="sd" data-title="اسراع" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li> <li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://sk.wikipedia.org/wiki/Zr%25C3%25BDchlenie" title="Zrýchlenie – Slovak" lang="sk" hreflang="sk" data-title="Zrýchlenie" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li> <li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://sl.wikipedia.org/wiki/Pospe%25C5%25A1ek" title="Pospešek – Slovenian" lang="sl" hreflang="sl" data-title="Pospešek" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li> <li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://szl.wikipedia.org/wiki/Szw%25C5%25AFng" title="Szwůng – Silesian" lang="szl" hreflang="szl" data-title="Szwůng" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target"><span>Ślůnski</span></a></li> <li class="interlanguage-link interwiki-so mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://so.wikipedia.org/wiki/Dardargelinta" title="Dardargelinta – Somali" lang="so" hreflang="so" data-title="Dardargelinta" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li> <li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ckb.wikipedia.org/wiki/%25D9%2584%25DB%2595%25D8%25B2" title="لەز – Central Kurdish" lang="ckb" hreflang="ckb" data-title="لەز" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li> <li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://sr.wikipedia.org/wiki/%25D0%25A3%25D0%25B1%25D1%2580%25D0%25B7%25D0%25B0%25D1%259A%25D0%25B5" title="Убрзање – Serbian" lang="sr" hreflang="sr" data-title="Убрзање" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li> <li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://sh.wikipedia.org/wiki/Ubrzanje" title="Ubrzanje – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Ubrzanje" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li> <li class="interlanguage-link interwiki-su mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://su.wikipedia.org/wiki/Aksel%25C3%25A9rasi" title="Akselérasi – Sundanese" lang="su" hreflang="su" data-title="Akselérasi" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li> <li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://fi.wikipedia.org/wiki/Kiihtyvyys" title="Kiihtyvyys – Finnish" lang="fi" hreflang="fi" data-title="Kiihtyvyys" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li> <li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://sv.wikipedia.org/wiki/Acceleration" title="Acceleration – Swedish" lang="sv" hreflang="sv" data-title="Acceleration" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li> <li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://tl.wikipedia.org/wiki/Arangkada" title="Arangkada – Tagalog" lang="tl" hreflang="tl" data-title="Arangkada" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li> <li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ta.wikipedia.org/wiki/%25E0%25AE%25AE%25E0%25AF%2581%25E0%25AE%259F%25E0%25AF%2581%25E0%25AE%2595%25E0%25AF%258D%25E0%25AE%2595%25E0%25AE%25AE%25E0%25AF%258D" title="முடுக்கம் – Tamil" lang="ta" hreflang="ta" data-title="முடுக்கம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li> <li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://tt.wikipedia.org/wiki/%25D0%25A2%25D0%25B8%25D0%25B7%25D0%25BB%25D3%2599%25D0%25BD%25D0%25B5%25D1%2588" title="Тизләнеш – Tatar" lang="tt" hreflang="tt" data-title="Тизләнеш" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li> <li class="interlanguage-link interwiki-te mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://te.wikipedia.org/wiki/%25E0%25B0%25A4%25E0%25B1%258D%25E0%25B0%25B5%25E0%25B0%25B0%25E0%25B0%25A3%25E0%25B0%25AE%25E0%25B1%2581" title="త్వరణము – Telugu" lang="te" hreflang="te" data-title="త్వరణము" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li> <li class="interlanguage-link interwiki-th mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://th.wikipedia.org/wiki/%25E0%25B8%2584%25E0%25B8%25A7%25E0%25B8%25B2%25E0%25B8%25A1%25E0%25B9%2580%25E0%25B8%25A3%25E0%25B9%2588%25E0%25B8%2587" title="ความเร่ง – Thai" lang="th" hreflang="th" data-title="ความเร่ง" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li> <li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://tr.wikipedia.org/wiki/%25C4%25B0vme" title="İvme – Turkish" lang="tr" hreflang="tr" data-title="İvme" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li> <li class="interlanguage-link interwiki-tyv mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://tyv.wikipedia.org/wiki/%25D0%2594%25D2%25AF%25D1%2580%25D0%25B3%25D0%25B5%25D0%25B4%25D1%258D%25D1%258D%25D1%2588%25D0%25BA%25D0%25B8%25D0%25BD" title="Дүргедээшкин – Tuvinian" lang="tyv" hreflang="tyv" data-title="Дүргедээшкин" data-language-autonym="Тыва дыл" data-language-local-name="Tuvinian" class="interlanguage-link-target"><span>Тыва дыл</span></a></li> <li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://uk.wikipedia.org/wiki/%25D0%259F%25D1%2580%25D0%25B8%25D1%2581%25D0%25BA%25D0%25BE%25D1%2580%25D0%25B5%25D0%25BD%25D0%25BD%25D1%258F" title="Прискорення – Ukrainian" lang="uk" hreflang="uk" data-title="Прискорення" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li> <li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://ur.wikipedia.org/wiki/%25D8%25A7%25D8%25B3%25D8%25B1%25D8%25A7%25D8%25B9" title="اسراع – Urdu" lang="ur" hreflang="ur" data-title="اسراع" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li> <li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://vec.wikipedia.org/wiki/Acelerasion" title="Acelerasion – Venetian" lang="vec" hreflang="vec" data-title="Acelerasion" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li> <li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://vep.wikipedia.org/wiki/Pigustuz" title="Pigustuz – Veps" lang="vep" hreflang="vep" data-title="Pigustuz" 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://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://vi.wikipedia.org/wiki/Gia_t%25E1%25BB%2591c" title="Gia tốc – Vietnamese" lang="vi" hreflang="vi" data-title="Gia tốc" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li> <li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://fiu-vro.wikipedia.org/wiki/Kip%25C3%25B5ndus" title="Kipõndus – Võro" lang="vro" hreflang="vro" data-title="Kipõndus" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li> <li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://zh-classical.wikipedia.org/wiki/%25E5%258A%25A0%25E9%2580%259F%25E5%25BA%25A6" title="加速度 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="加速度" 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-war mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://war.wikipedia.org/wiki/Akselerasyon" title="Akselerasyon – Waray" lang="war" hreflang="war" data-title="Akselerasyon" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li> <li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://wuu.wikipedia.org/wiki/%25E5%258A%25A0%25E9%2580%259F%25E5%25BA%25A6" title="加速度 – Wu" lang="wuu" hreflang="wuu" data-title="加速度" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li> <li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://yi.wikipedia.org/wiki/%25D7%25A4%25D7%2590%25D7%25A8%25D7%2592%25D7%2599%25D7%259B%25D7%25A2%25D7%25A8%25D7%2595%25D7%25A0%25D7%2592" title="פארגיכערונג – Yiddish" lang="yi" hreflang="yi" data-title="פארגיכערונג" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li> <li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://yo.wikipedia.org/wiki/%25C3%258Cy%25C3%25A1ra" title="Ìyára – Yoruba" lang="yo" hreflang="yo" data-title="Ìyára" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li> <li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://translate.google.com/website?sl=en&tl=ja&hl=ja&u=https://zh-yue.wikipedia.org/wiki/%25E5%258A%25A0%25E9%2580%259F%25E5%25BA%25A6" title="加速度 – Cantonese" lang="yue" hreflang="yue" data-title="加速度" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li> <li class="interlanguage-link interwiki-zh mw-list-item"><a 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