A space vehicle deploys its re-entry parachute when it's traveling at a vertical velocity of -150 meters/second (negative because the parachute is going down.) It comes to rest at 0 meters/second after 30 seconds. What's the average acceleration of the shuttle during this time span?

The initial velocity is -150m/s.
Remember that:
V(t) = Vi + at, where v(t) is velocity at time t, Vi is initial velocity, and a is acceleration.
We know that the vehicle stopped after 30 seconds, so V(30) = 0.
Let's plug the useful info into our function and solve for a:
0 = -150 + a*30     Add 150 to both sides
150 = 30a             Divide both sides by 30
a = 5 m/s²
The average acceleration is 5 meters per second squared.