Instantaneous Acceleration
<p style="margin: 0.5em 0px 1em; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">Instantaneous acceleration, meanwhile, is the <a href="https://en.m.wikipedia.org/wiki/Limit_of_a_function" title="Limit of a function" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161);">limit</a> of the average acceleration over an <a href="https://en.m.wikipedia.org/wiki/Infinitesimal" title="Infinitesimal" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161);">infinitesimal</a> interval of time. In the terms of <a href="https://en.m.wikipedia.org/wiki/Calculus" title="Calculus" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161);">calculus</a>, instantaneous acceleration is the <a href="https://en.m.wikipedia.org/wiki/Derivative" title="Derivative" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161);">derivative</a> of the velocity vector with respect to time:</p><dl style="margin: 0px 0px 0px 1em; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;"><dd style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; overflow: auto;"><span class="mwe-math-element" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline;"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; display: none; clip: rect(1px, 1px, 1px, 1px); overflow: hidden; position: absolute; width: 1px; height: 1px; opacity: 0;"><math 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><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><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57df7a9fae2d9253e99e9433874ab522ce31a428" class="mwe-math-fallback-image-inline" aria-hidden="true" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: -2.171ex; display: inline-block; width: 19.957ex; height: 5.676ex;"></span><span style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline;"></span></dd></dl><p style="margin: 0.5em 0px 1em; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline;">(Here and elsewhere, if <a href="https://en.m.wikipedia.org/wiki/Rectilinear_motion" title="Rectilinear motion" class="mw-redirect" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161);">motion is in a straight line</a>, <a href="https://en.m.wikipedia.org/wiki/Euclidean_vector" title="Euclidean vector" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161);">vector</a> quantities can be substituted by <a href="https://en.m.wikipedia.org/wiki/Scalar(physics)" title="Scalar (physics)" style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-align: baseline; color: rgb(107, 75, 161);">scalars</a> in the equations.)</p>