Chapter 4.6, Problem 32ES

A position function of a particle moving along a coordinate line is given. Use the method of Example $6$ to analyze the motion of the particle for $t\ge 0,$ and give a schematic picture of the motion (as in Figure $\mathrm{4.6.8}$ ).

$s=\left\{\begin{array}{cc}2t{\left(t-2\right)}^2,& 0\le t<3\\ 13-7{\left(t-4\right)}^2,& t\ge 3\end{array}\right.$