A particle moves in a straight line, so that t seconds, after leaving a fixed-point O, its velocity, v ms^-1, is given by v = pt² + qt – 12, where p and q are constants.

When t = 2 the acceleration of the particle is 18 ms^-2.

When t = 4 the displacement of the particle from O is 32 m.

Find the value of p and the value of q.