Chapter 12, Problem 34RE

To determine

To prove: That the rate of change of speed of a particle can be expressed as $\frac{d}{dt}\left(‖v‖\right)=\frac{1}{‖v‖}\left(v\cdot a\right)$ , where $v=v\left(t\right)$ and $a=a\left(t\right)$ are the velocity and acceleration vectors of a particle moving in the $2\text{-space}$ or $3\text{-space}$ .