I read in a book under the definition of power. I’ll give it in the same words. “Work done does not depend on time. For example, If a person A lifts 10 kg load through 5 ft in 2 minutes and person B lifts the same load through the same height in 1 minute, the work done by both the persons is the same, but the rate at which the work is done is not the same. We say that the second person is stronger and has more power. Thus power is defined as the rate of work done.” Now since the work done is same and Work = F x s , F x s is same for both A and B. Since the height to which the persons lift the load is the same, the displacement is the same. So F1 = F2. But F = ma. Since the mass of the body is same, a1 = a2. If the acceleration is the same, then why does A take more time to lift the same body from the ground than B? Has it got something to do with gravity? Can you please explain this?

Displacement is independant of force, so you cannot reason that since d1=d2, F1=F2, and it is this force which will determine the power. So, the acceleration is not the same, and no, gravity has nothing to do with that. -Andrew

Another thing to consider: Since the work done in the lifting is W=Fs and average Power = W/t, where t is the time taken, we have for the average power P = F s/t = Fv where v is the average speed at which the weight is lifted and F is the average force applied. So, lifting faster requires more power. Of course, a real lift does not happen at constant speed. The mass must be accelerated from rest, lifted and (presumably) decelerated to rest at the top of the lift. So, the force is not constant and neither is the instantaneous power. At certain times during the lift, the instantaneous power of the lifting force will be less than the average power; at other times it will be greater. But these details don't affect the argument about the average given above.