On the formula of acceleration of gravity How is h = 1 / 2GT ^ 2 derived? I know T2 is about S2 in G, but what about half?

On the formula of acceleration of gravity How is h = 1 / 2GT ^ 2 derived? I know T2 is about S2 in G, but what about half?


V = V0 + at (end velocity = initial velocity plus acceleration times time) d = 1 / 2 (V0 + V) t (distance = average velocity plus time) merge d = 1 / 2 (V0 + V0 + at) td = 1 / 2 (2v0 + at) td = v0t + 1 / 2at ^ 2 free fall, V0 = 0d = 1 / 2at ^ 2A = acceleration of gravity = GD = height = H