Chapter 1.4, Problem 21P

To determine

(a)

To show:

The equation ${\tan }^{-1}\left(v\right)={\tan }^{-1}\left(v_o\right)-t$ and to prove that the object comes to rest after a finite time ${\tan }^{-1}\left(v_o\right)$ and to check if the object remain at rest.

To determine

(b)

To show:

The equation $\frac{dv}{dt}=-\left(1+v^2\right)$ can be written as $v\frac{dv}{dx}=-\left(1+v^2\right)$ by using chain rule and to determine the distance travelled by the object when it comes to rest.