Determining distance traveled from velocity

A toy rocket is launched vertically from the ground on a day with no wind. The rocket's vertical velocity at time $t$ (in seconds) is given by $v(t)= 500-32t$ feet/sec.

1. At what time after the rocket is launched does the rocket's velocity equal zero? Call this time value $a$. What happens to the rocket at $t = a$?

2. Find the value of the total area enclosed by $y = v(t)$ and the $t$-axis on the interval $0 \le t \le a$. What does this area represent…