Question

If the force acting on a body is inversely proportional to it's velocity, then the kinetic energy acquired by the body in time $t$ is proportional to :

• A. $t^0$
• B. $t^1$
• C. $t^2$
• D. $t^4$

Answer 1

Answer: (B)

$t^1$

Given $F\propto \frac{1}{v}$
Work done on the body is converted to kinetic energy.
$W=F.s=KE$
$\Rightarrow KE\propto \frac{1}{v}.s$
$KE\propto \frac{s}{v}=\frac{s}{s/t}=t$
$\Rightarrow KE\propto t$
Option B.