The relationship between acceleration, velocity and displacement is general and holds in any number of dimensions.
In two dimensions the displacements in the
and
directions are generally expressed as functions of
with thecomponent labelled with
and 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.
If
with
then
Then if
