S is proportional to t3 (s=1/2at2 where u=0 and p=mav a=p/mv Put this in the first equation and get the answer)

Introduction:
When a body is being moved from rest along a straight line by a machine delivering constant power, the distance covered by the body in time t is proportional to the square of time t. This relationship can be explained by understanding the concept of power, work, and energy.

Power:
Power is defined as the rate at which work is done or energy is transferred. It is given by the equation P = W/t, where P represents power, W represents work, and t represents time.

Work:
Work is defined as the product of force and displacement. It is given by the equation W = F * d, where W represents work, F represents force, and d represents displacement.

Energy:
Energy is the ability to do work. It exists in various forms such as kinetic, potential, thermal, etc. In this scenario, we are concerned with kinetic energy, which is the energy possessed by a body due to its motion. Kinetic energy is given by the equation KE = (1/2) * m * v^2, where KE represents kinetic energy, m represents mass, and v represents velocity.

Explanation:
1. When a body is at rest and a machine starts moving it, the initial velocity of the body is zero.
2. As the machine delivers constant power, the force applied on the body remains constant.
3. The work done on the body by the machine is given by the equation W = F * d.
4. As the body starts moving, it covers a certain distance in time t.
5. Since the force and displacement are in the same direction, the work done on the body is positive.
6. The work done on the body increases its kinetic energy, as work done is directly related to the change in kinetic energy.
7. The increase in kinetic energy is proportional to the square of the velocity, as shown in the equation KE = (1/2) * m * v^2.
8. As the body covers more distance, its velocity increases.
9. The distance covered by the body in time t is directly related to the change in kinetic energy, which is proportional to the square of the velocity.
10. Therefore, the distance covered by the body in time t is proportional to the square of time t.

Conclusion:
In conclusion, when a body is being moved from rest along a straight line by a machine delivering constant power, the distance covered by the body in time t is proportional to the square of time t. This relationship arises from the concept of power, work, and energy, where the work done on the body increases its kinetic energy, leading to an increase in velocity and distance covered.