Question

An object moves on the x-axis in such a way that its velocity and displacement from the origin satisfy the relation v = – kx, where k is a positive constant. Show that the object does not change its direction and the kinetic energy of the object keeps on decreasing.

Answer 1

(a) Let A be positive. At t = 0, x = A and as t increases x decreases continuously and after a long time x becomes zero.

(b) Let A be negative. and as t increases x increases continuously from the negative value and after a long time it becomes zero. So the object does not change its direction. The kinetic energy of the object is

which decreases with time.