Model rocket (velocity and time equation help please)

[Duke77]

A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t)=60t, at which time the fuel is exhausted and it becomes a freely “falling” body. Fourteen seconds after the fuel is exhausted, the rocket’s parachute opens, and the (downward) velocity slows linearly to -18 ft/sec in 5 seconds. The rocket then “floats” to the ground at that rate. Find the position function s and the velocity function v for any time t, then sketch the graphs of s and v.

This is the whole question and I don't expect help with the graphs but if I could get some help on the problem I would appreciate it greatly.

[Doc Al]

Attack it step by step.

For T = 0, 3 secs: Integrate the acceleration function (twice) to find expressions for v and s.
For T = 3, 14 secs: It's a projectile. Uniform acceleration due to gravity.
For T = 14, 19 secs: the acceleration is given
For T > 19 secs: uniform speed

It's a pain in the butt, but you can do it!