A block of mass m is acted upon by a constant horizontal for...

Question

A block of mass m is acted upon by a constant horizontal force F on a horizontal surface, starting from rest. The block moves a distance d before the force F is removed. After the force is removed, the block continues to move and travels a distance 2d before coming to rest. What is the magnitude of the frictional force f acting on the block?

1. Work Done by the Applied Force:

When the force is applied, the block accelerates and moves a distance . The work done by the applied force is:

2. Work Done by the Frictional Force:

After the force is removed, the block moves a distance before stopping, so the total distance is d + 2d = 3d. The work done by the frictional force is negative because it opposes the motion:

According to the work - energy theorem, the net work done on the object is equal to the change in its kinetic energy.

The block starts from rest and comes to rest, so the change in kinetic energy

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