# 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.

graph LR A(Displacement) --->|Differentiation| B(Velocity) --->|Differentiation| C(Acceleration) C --->|Integration| B --->|Integration| A

### Formulae

Variable Key

is displacement. is velocity. is acceleration. is time.