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_{i}T + 0.5at

^{2}to calculate the acceleration (by assuming the initial velocity is 0) which allowed them to calculate the force [ma], and use that force to calculate work [Fd]. For this method, how quickly you move the weight impacts the work done (shorter time means more acceleration which means more force and more work).

Others looked at the change in potential energy [mgh] and in this method how quickly you move the weight does not matter [for work, though obviously the power is different]. The second method makes sense to me, but I can't get my head around how the difference in acceleration in the first method doesn't change the work. I feel like I am missing something basic. Any help is greatly appreciated.