The relationship between displacement, velocity and acceleration is more general than given by the suvat equations, or the simple equations of motion. These equations only for constant acceleration, but the acceleration is often not constant in general. The general relationships are illustrated below.
So for example suppose we have the velocity and we need to find the acceleration. We differentiate. If we want to find the displacement, we integrate.
Example:
a) Find the acceleration when
b) Find the displacement s as a function of time if
a)
so when
b}
We are told that
when
so
