The physics
Power is how fast a force does work. One watt is one joule each second.
P = W / t P = F v
A winch lifts a load at a steady speed. Its work is mgh, so its power is mgh / t. On a rough slope at a steady speed, the pull balances two forces. They are mg sin θ and friction, μ mg cos θ.
P = (mg sin θ + μ mg cos θ) v
A steady force on a cart from rest gives it more and more speed. So its power, F v, grows with time. The average power is the whole work over the whole time. A rope at an angle θ works only through F cos θ.
A pump wastes some of its power. Its efficiency η is the useful share. So the input power is the useful power divided by η.
Pin = Puseful / η
A motor at a fixed power P does work Pt. From rest, with no friction, that work becomes KE. So v grows as √t, and the kart covers (2/3)vt.
P t = ½ m v² x = (2/3) v t