Chapter 7.9, Problem 62E

a.

To determine

To show: The equation $f\left(v\right)=-k{v}^2$ can be written in the form $v\text{'}\left(t\right)=g-a{v}^2$ where $a=\frac{k}{m}$.

b.

To determine

To find: The terminal velocity, that is the value of v such that $v\text{'}\left(t\right)=0$.

c.

To determine

To find: The solution of the given separable equation with initial value $v\left(0\right)=0$ and $0<v{\left(t\right)}^2<\frac{g}{a}$ for $t\ge 0$.

d.

To determine

To verify: The terminal velocity satisfy with the value found in part (b) and the graph of the given function for $g=9.8{\text{m/s}}^{\text{2}}$, $m=1$ kg and $k=0.1$ kg/m.