If the force acting on a body is inversely proportional to its speed, then the Kinetic Energy of the body is

given that force acting on an object F is inversely proportional to its speed

(instantaneous velocity) V

$\text{F}\propto \frac{\text{1}}{\text{V}}$

FV = constant K                     $\text{V}=\frac{\Delta \text{s}}{\Delta \text{t}}$

$\text{FV}=\text{F}\frac{\Delta \text{s}}{\Delta \text{t}}=\text{K}$

$\text{F\hspace{0.17em}}\Delta \text{s}=\text{K\hspace{0.17em}}\Delta \text{t}$= work done = change in K.E

$\Delta \text{\hspace{0.17em}KE}=\text{K\hspace{0.17em}}\Delta \text{t}$

Let t = 0      K.E = 0

t = t      $\text{K.E}=\frac{1}{2}{\text{mv}}^{\text{2}}$

then we can have $\frac{\text{1}}{\text{2}}{\text{mv}}^{\text{2}}=\text{K.t}$

So we can claim K.E is directly proportional to time.

Option (b) is correct conclusion

Where as option a, c, d are incorrect.