acceleration

From Physics wiki

Acceleration is defined to be the rate of change of velocity of an object with respect to time. During an interval of time $\Delta t = t_2 - t_1\,$ in which the velocity changes by an amount $\Delta v= v_2 - v_1\,$ , the average acceleration is defined by

$a_{avg} \equiv \frac{\Delta v}{\Delta t} = \frac{v_2 - v_1}{t_2 - t_1}\,$ .

By considering smaller and smaller intervals $\Delta t\,$ , we define the instantaneous acceleration by

$a = \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t} = \frac{v(t+\Delta t) - v(t)}{\Delta t}\,$ ,

which is the derivative of velocity with respect to time:

$a \equiv \frac{dv}{dt}\,$ ,

or, in terms of position,

$a \equiv \frac{d^2x}{dt^2}\,$ .

Usually instantaneous acceleration is simply called acceleration. The dimensions of acceleration are length/time² and the corresponding units are $m/s^2\,$ .