Kinetic Energy - derivation
KE(m,v) = mgh (The amount of kinetic energy, which depends on the quantities mass and speed in this case equals the amount of work done by gravity, mgh).
From our motion equations, v = vo + gt and
h = ho + vot + (1/2)gt2 or in this case (ho=0, vo=0): h = (1/2)gt2, or t = (2h/g)1/2 so v = gt = g(2h/g)1/2, or v = (2hg)1/2, or h = (1/2)v2/g; thus mgh = mg(1/2)v2/g = (1/2)mv2 = KE .