Force and Power?

Question

Is there a universal relationship between Force and Power and if there is what's the formula that describes this relationship?

This is related to a prior question that I asked today.

Answer 1

Force: how hard you push to get a rock up hill F=MA

Energy: How high you push the rock  PE= MAH = FH

Power: How fast you pushed the rock up the hill, 1 second? 1 minute? 1 hour?  etc Power = PE/t = FH/t

Now there are other formulations for different forms of Force, Energy, and Power, but this is the basic idea

Answer 2

Yes - Power = work/time = W/t

Work = Force acting over some distance = F*d

Power = F*d/t  

But distance over time = speed = v

Power = F*v   where v = speed of the body work is being done on.

Answer 3

Yes, there is a universal relation between power and force

power = dW/dt....rate at which work is done with respect to time

but dW = force * displacement(i time dt) = f*ds

thus p = dW/dt = f*ds/dt

but ds/dt = velocity = v

thus p = f*v