Chapter 2.1, Problem 3QCE

A particle is moving along an $s\text{-axis}$ , where $s$ is in feet. During the first $5$ seconds of motion, the position of the particle is given by

$s=10-{\left(3-t\right)}^2,0\le t\le 5$

Use this position function to complete each part.

(a) Initially, the particle moves a distance of $\text{\_\_\_\_\_\_\_}$ ft in the (positive/negative) $\text{\_\_\_\_\_\_\_}$ direction; then it reverses direction, traveling a distance of $\text{\_\_\_\_\_\_\_}$ ft during the remainder of the $5$ -second period.

(b) The average velocity of the particle over the $5$ -second period is $\text{\_\_\_\_\_\_\_}$ .