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Let the stone of mass m be at a height h and be dropped from rest at t = 0 sec.

Initial potential energy = PE1 = m g h
initial kinetic energy = 1/2 m 0^2 = 0

Let the stone drop by a distance s in time  t.  As per the laws of kinetics we have
       2 g s = (v^2 - u^2 ) = v^2

Potential energy at time t and height of (h - s) is   PE2 = m g (h - s)
Kinetic energy = KE2 = 1/2 m v^2 = 1/2 m (2 g s) = m g s

Total energy = m g (h - s) + m g s = m g  h

All along the path ,  from t = o to  t = root(2h/g) ,  and height h to 0, the total energy remains as  m g h.

The other forms of energy in the object are assumed to be constant and not varying.

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