Acceleration

Acceleration describes how velocity changes with time.

Average Acceleration

$$ a_{\text{avg}} = \frac{\Delta v}{\Delta t} $$

Instantaneous Acceleration

$$ a = \frac{dv}{dt} $$

Or:

$$ a = \frac{d^2 x}{dt^2} $$

In vector form:

$$ \vec{a} = \frac{d^2 \vec{r}}{dt^2} $$