# How do velocity and acceleration differ?

Mar 30, 2018

See below:

#### Explanation:

Common calculus problems involve displacement-time functions,
$d \left(t\right)$. For the sake of the argument let's use a quadratic to describe our displacement function.

$d \left(t\right) = {t}^{2} - 10 t + 25$

Velocity is the rate of change of displacement- the derivative of a $d \left(t\right)$ function yields a velocity function.

$d ' \left(t\right) = v \left(t\right) = 2 t - 10$

Acceleration is the rate of change of velocity- the derivative of a $v \left(t\right)$ function or the second derivative of the $d \left(t\right)$ function yields an acceleration function.

$d ' ' \left(t\right) = v ' \left(t\right) = a \left(t\right) = 2$

Hopefully, that makes their distinction clearer.