Chapter 1.1, Problem 9E

Reminder Round all answers to two decimal places unless otherwise indicated.

Note Some of the formulas below use the special number $e$, which was presented in the Prologue.

V, in feet per second, is a function of the time t, in seconds, since the ball was thrown. The formula is

$V=40-32t$

if we ignore air resistance. The function V is positive when the ball is rising and negative when the ball is falling.

a. Express using functional notation the velocity $1$ second after the ball is thrown, and then calculate that value. Is the ball rising or falling then?

b. Find the velocity $2$ seconds after the ball is thrown. Is the ball rising or falling then?

c. What is happening $1.25$ seconds after the ball is thrown?

d. By how much does the velocity change from $1$ to $2$ seconds after the ball is thrown? From $2$ to $3$ seconds? From $3$ to $4$ seconds? Compare the answers to these three questions and explain in practical terms.