Force acting on a particle moving in a straight line varies with the velocity of the particle as F=k/v,where K is a constant.The work done by this force in time t is:

(A)K/v^2.t

(B)2Kt

(C)Kt

(D)2Kt/v^2

we are given

F = ma = K/v

or

m(dv/dt) = K/v

or

mvdv = Kdt

now integrating both sides

v varies form v₁ to v₂ while t from 0 to t, so

m(v₂²/2 - v₁²/2) = Kt

so,

(1/2)mv₂²/2 - (1/2)mv₁² = Kt

thus,

change in KE = Kt

now, from work energy theorem 

change in KE = work done

thus,

work done, W = Kt

correct answer is (c)