Exercise 8

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 in terms of the physical setting of the problem?

3. Find an antiderivative $s$ of the function $v$. That is, find a function $s$ such that $s'(t) = v(t)$.

4. Compute the value of $s(a) - s(0)$. What does this number represent in terms of the physical setting of the problem?

5. Compute $s(5) - s(1)$. What does this number tell you about the rocket's flight?