Motion Graphs and Calculus

We know that velocity is change in displacement, and acceleration is change in velocity. Calculus tells us that the rate of change of a function is the derivative, and therefore we can differentiate and integrate to convert between different functions of displacement, velocity and acceleration.

Formulae

v = \frac{d s}{d t} a = \frac{d v}{d t}

v = \int a d t s = \int v d t

Variable Key

$s$ is displacement.
$v$ is velocity.
$a$ is acceleration.
$t$ is time.