A 10 kg box slides horizontally without friction at a speed of 1 m/s. At one point, a constant force is applied to the box in the direction of its motion. The box travels 5 m with the constant force applied. The force is then removed, leaving the box with a speed of 2 m/s. What is the magnitude of the applied force

Fapp = 3 N

Explanation:

Applying the work-energy theorem, we know that the net work done on one object by an applied force, is equal to the change in the kinetic energy of the object.This work is just the product of the applied force times the displacement, as follows:

       

This must be equal to the change in kinetic energy:

       

Equating (1) and (2),  and replacing by the givens, we can solve for Fapp, as follows:

       

The  magnitude of the applied force is 3 N.