This problem is on a worksheet my class has to do, and I can't figure it out. I can do these types of problems normally, but the piecewise part is what's screwing me up.

A rocket is launched with an initial velocity of zero, and with acceleration in feet per second per second defined by:
a(t)={20e^(-t/2), for 0=t=10 seconds
{-16, for t>10 seconds

a. At what time does the rocket begin to descend?
b. How high does the rocket reach?
c. What is the velocity when the rocket impacts the earth?
d. Write a formula for the position of the rocket with respect to time for t>10 seconds

any help is greatly appreciated! thanks :)

View the original article here