A rock is lifted for a certain time by a force F that is greater in magnitude than the rock's weight mg. The change in kinetic energy of the rock during this time is equal to the

The change in kinetic energy of the rock during this time is equal to the work done on the rock.

The work done on an object is equal to the force applied to the object multiplied by the distance over which the force is applied. In this case, the force applied to the rock is F and the distance over which the force is applied is the height to which the rock is lifted (h).

So, the work done on the rock (W) is equal to Fh.

However, the force F is greater than the weight of the rock (mg), so the net force on the rock is F - mg.

Therefore, the work done on the rock is (F - mg)h.

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

Therefore, the change in kinetic energy of the rock is (F - mg)h.