Exercise 8

The velocity of a ball that has been tossed vertically in the air is given by $v(t) = 16 - 32t$, where $v$ is measured in feet per second, and $t$ is measured in seconds. The ball is in the air from $t = 0$ until $t = 2$.

1. When is the ball's velocity greatest?

2. Determine the value of $v'(1)$. Justify your thinking.

3. What are the units on the value of $v'(1)$? What does this value and the corresponding units tell you about the behavior of the ball at time $t = 1$?

4. What is the physical meaning of the function $v'(t)$?