Problem 37.

A displacement, s, of an object as a function of time, t, is given by

a) Find an expression for the acceleration of the object

b) Explain why this expression indicates that the acceleration is not constant

Solution:

(a) Acceleration is the second derivative of displacement with respect to time.

The first derivative of displacement with respect to time is a velocity:

The derivative of the velocity is an acceleration:

(b) From this expression we can see that the acceleration depends on time (at different moments of time we have different acceleration) – it means that acceleration is not constant.