Chapter 4.6, Problem 16ES

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

(a) Make a table showing the position, velocity, and acceleration to two decimal places at times $t=1,2,3,4,5$ .

(b) At each of the times in part (a), determine whether the particle is stopped; if it is not, state its direction of motion.

(c) At each of the times in part (a), determine whether the particle is speeding up, slowing down, or neither.

$s\left(t\right)=t^4{e}^{-t},t\ge 0$