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