What's the work done in an object to change its direction?

Question

Say, for example an object is moving 2m/s right and some force makes it travel 2m/s left. What would be the work done on this object? It starts and ends with the same kinetic energy, but clearly something had to be done to it to make it start moving left.

Answer 1

Let's assume the force acting to the left is constant.

For it to change the velocity from 2 m/s to the right to 2 m/s to the left the force must first decelerate the object to 0 m/s. That means the force did negative work on the object because the direction of the force is opposite to the movement of the object while it slows down. Net negative work decreases the kinetic energy of the object.

But since the force remains, it now accelerates the object from 0 m/s to 2 m/s to the left. Now the force is doing positive work since its direction is the same as the motion of the object. Net positive work increases the kinetic energy of the object.

The amount of negative work done by the force to decelerate the object to 0 m/s equals the amount of positive work done by the force to accelerate the object to 2 m/s, for a net work of zero. Per the work energy theorem the net work done on an object equals its change in kinetic energy. Since the net work is zero, the change in kinetic energy is zero.

Hope this helps.