A particle P moves in a straight line, starting from rest at a point O on the line. At time t s after leaving O the acceleration of P is k(16 - t^2) m s^-2, where k is a positive constant, and the displacement from O is s m. The velocity of P is 8 m s^-1 when t = 4.

1. Show that s = \frac{1}{64} t^2 (96 - t^2).
2. Find the speed of P at the instant that it returns to O.
3. Find the maximum displacement of the particle from O.