Acceleration

Acceleration is the vector representing the change in velocity with respect to time. It is usually represented with a. Its SI unit is m/s².

The integral of acceleration with respect to time is velocity, and its second integral is position.

Formulae

The formula for average acceleration on a linear path is change in velocity divided by change in time, or

$a_{ave} = \frac{v_1 - v_0}{t_1 - t_0} = \frac{\Delta v}{\Delta t}$

The instantaneous acceleration is equal to the derivative of velocity with respect to time.

$a = \lim_{{\Delta t} \to 0} \frac{\Delta v}{\Delta t} = \frac{d v}{d t}$