Chapter 12.6, Problem 29ES

The position vectors ${\text{r}}_1\text{and}{\text{r}}_2$ of two particles are given. Show that particles move along the same path but the speed of the first is constant and the speed of the second is not.

$\begin{array}{l}{\text{r}}_1=2\cos 3t\text{i}+2\sin 3t\text{j}\\ {\text{r}}_{\text{2}}=2\cos (t^2)\text{i}+2\sin (t^2)\text{j}(t\ge 0)\end{array}$