Chapter 4.6, Problem 21ES

The function $s\left(t\right)$ describes the position of a particle moving along a coordinate line, where s is in feet and $t$ is in seconds.

(a) Find the velocity and acceleration functions.

(b) Find the position, velocity, speed, and acceleration at time $t=1$ .

(c) At what times is the particle stopped?

(d) When is the particle speeding up? Slowing down?

(e) Find the total distance traveled by the particle from time $t=0$ to time $t=5$ .

$s\left(t\right)=\left(t^2+8\right)e^{-t/3},t\ge 0$