A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t) = 72t, at which time the fuel is exhausted and it becomes a freely "falling" body. Sixteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to -28 ft/s in 5 seconds. The rocket then "floats" to the ground at that rate. (a) Determine the position function s and the velocity function v (for all times t). 36+2 if Osts 3 -32t + 420 if 3 24 12+3 if Ost s 3 -1612 + 420t - 792 if 3 24