# How do velocity and acceleration differ?

May 3, 2018

Velocity and acceleration are two completely different quantities, but they are closely related to one another.

#### Explanation:

Velocity is the rate of change of position. Acceleration is the rate of change of velocity.

In other words, velocity will tell you how the position of an object is changing in time. Acceleration will tell you how the velocity of an object is changing in time.

In terms of calculus, we can formulate the following relation for a velocity function $v \left(t\right)$, and an acceleration function $a \left(t\right)$:

$\implies a \left(t\right) = \frac{\mathrm{dv} \left(t\right)}{\mathrm{dt}}$

or equivalently

$\implies v \left(t\right) = \int a \left(t\right) \mathrm{dt}$

The units of velocity are $\text{m"/"s}$
The units of acceleration are ${\text{m"/"s}}^{2}$