Chapter 12, Problem 29RE

Suppose that $\text{r}\left(t\right)$ is the position function of a particle moving in 2-space or 3-space. In each part, explain what the given quantity represents physically.

$\begin{array}{l}\left(\text{a}\right)‖\frac{d\text{r}}{dt}‖\\ \left(\text{b}\right){\displaystyle {\int }_{t_0}^{t_1}‖\frac{d\text{r}}{dt}‖}\\ \left(\text{c}\right)‖\text{r}\left(t\right)‖\end{array}$