Question

If the force acting on a body is inversely proportional to its speed, then its kinetic energy is:

• A. Linearly related to time
• B. Inversely proportional to time
• C. Inversely proportional to the square of time
• D. A constant

Answer 1

The correct option is A Linearly related to time

$F\propto \frac{1}{v},F=\frac{C}{v}$
Where $C$ is a constant of proportionality.
$\Rightarrow ma=\frac{C}{v}$ or $m\frac{dv}{dt}=\frac{C}{v}$
$vdv=\frac{Cdt}{m}$
Integrating both sides, we get
$\frac{v^2}{2}=\frac{Ct}{m}$ or $\frac{1}{2}m{v}^2=Ct$
or Kinetic energy, $K=\frac{1}{2}m{v}^2=Ct$ or $K\propto t$.