Force acting on a particle moving in a straight line varies with velocity of the particle as $F = \frac{k}{v}$ , k is a constant. The work done by this force in time t is : (At t=0, particle is moving with non zero speed)

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$\frac{k}{v^{2}} t$

$2 k t$

$k t$

$\frac{2 k t}{v^{2}}$

answer is C.

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Detailed Solution

Given
$F o r c e, F = \frac{k}{v} \Rightarrow m \frac{d v}{d t} = \frac{k}{v} \Rightarrow \int_{u}^{v} v d v = \frac{k}{m} \int_{0}^{t} d t$
$\Rightarrow \frac{m}{2} (v^{2} - u^{2}) = k t$

As per work energy theorem , change in kinetic energy is work done by the force.

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