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Displacement, Velocity and Acceleration

The relationship between displacement, velocity and acceleration are much more general than is given by the suvat equations, or the simple equations of motion. These equations only apply for constant acceleration, but in fact the acceleration is not constant in general. The general relationships are illustrated below.

So for example suppose we have the velocity and we want to find the acceleration. We differentiate. If we have the velocity and 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 thatwhenso