Option 1: Linearly with square root of time.

If the rate of change of kinetic energy varies linearly with the square root of time, it means that as time increases, the rate of change of kinetic energy also increases, but at a decreasing rate. This option suggests that the kinetic energy of the body would increase, but at a slower and slower rate as time goes by. However, this option does not accurately describe the situation described in the question, as the rate of change of kinetic energy is not related to the square root of time.

Option 2: Linearly with time.

This is the correct answer. When a constant force is applied to a body initially at rest, the rate of change of its kinetic energy increases linearly with time. This means that as time goes on, the kinetic energy of the body increases at a steady rate.

Option 3: Linearly with square of time.

If the rate of change of kinetic energy varies linearly with the square of time, it means that the kinetic energy of the body would increase at an accelerating rate. This option does not accurately describe the situation described in the question, as the rate of change of kinetic energy is not related to the square of time.

Option 4: Inversely with time