theory behind formulas?

Question

I'm trying to find out people's thoughts as to the theories behind these formulas: Ek = 0.5mv^2, Ep = mgh, and P=W/t. Any good guesses?

Answer 1

The kinetic energy (Ek) and potential energy (Pk) equations can be derived by calculating the amount of work done on the body. The gravitational potential energy calculation is very simple, as the force (mg) is constant, and the work (energy) is simply force times distance. You can derive the kinetic energy equation from Newton's second law:
For constant acceleration from 0:
v = at and d = 1/2 at^2
E = Fd = ma·at^2/2 = 1/2 m · (at)^2
and since at = v, E = 1/2 mv^2.
P=W/t is just the definition of power; there's nothing to derive or prove.