This is where we have to admit that gravitational potential energy is one of those things that depends on the "frame of reference", or 'relative to what?'.
Potential energy = (mass) x (gravity) x (<em>height</em>).
So you have to specify <em><u>height above what</u></em> .
-- With respect to the ground, the ball has zero potential energy. (If you let go of it, it will gain zero kinetic energy as it falls to the ground.)
-- With respect to the floor in your basement, the potential energy is
(3) x (9.8) x (3 meters) = 88.2 joules.
(If you let go of it, it will gain 88.2 joules of kinetic energy as it falls to the floor of your basement.)
-- With respect to the top of that 10-meter hill over there, the potential energy is (3) x (9.8) x (-10) = -294 joules
(Its potential energy is negative. After you let go of it, you have to give it 294 joules of energy that it doesn't have now, in order to lift it to the top of the hill <em>where it will have zero</em> potential energy.)
False we can calculate it at a specific time by taking the derivative of positive function, which gives us the functional form of instantaneous velocity v(t)
