The General Relationship Between Displacement, Velocity and Acceleration

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

Suppose we have the velocity. To find the acceleration we differentiate and to find the displacement, we integrate.


a) Find the acceleration when

b) Find the displacement s as a function of time if

a) so when


We are told thatwhenso