Chapter 4.6, Problem 31ES

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 $\mathrm{4.6.8}$ ).

$s=\left\{\begin{array}{cc}\cot t,& 0\le t<2\pi \\ 1,& t\ge 2\pi \end{array}\right.$