Working with position functions using acceleration and velocity.

A model rocket is fired vertically upward from rest. It's acceleration for the first three seconds is a(t)=60t at which time the fuel is exhausted and it becomes a free falling body. After 17 seconds, the rocket's parachute opens and the velocity slows linearly to -18 ft/sec in 5 seconds. The rocket then floats to the ground at that rate.

a) Find the position function s and the velocity function v for all times t. Sketch the graphs of s and v.

b) At what time does the rocket reach its maximum height?

c) At what time does the rocket hit the ground?

Recall that acceleration due to gravity is

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...t) and the acceleration a(t).
s'(t)=v(t), v'(t)=a(t) and s"(t)=a(t). ...