## Acceleration, Velocity and Displacement in Two Dimensions

The relationship between acceleration, velocity and displacement is general and holds in any number of dimensions.

In two dimensions the displacements in theanddirections are generally expressed as functions ofwith thecomponent labelled withand thecomponent labelled with

If

then velocity is found by differentiation of (the components of) displacement:and the acceleration is found by differentiation of the components of velocity:

Conversely, given the acceleration, the velocity is found by integration, and the displacement is found by integrating the velocity.

Ifwiththen

Then if