Question

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

Answer 1

as you know,
work done = integral of force multiplied by velocity.
then we will get the answer as W = kt

Answer 2

Answer:

The work done by this force in time t is Kt.

Explanation:

Since work done is defined as the force times displacement.

$W.D=\int\ F \, ds$........................(1)

Where ds is the displacement.

We know that the velocity is the rate of change of displacement.

$V = \dfrac{ds}{dt}$.....................(2)

From (1) and (2) we get,

$W.D=\int\ {FV} \, dt$....................(3)

We have Force

$F=\dfrac{K}{V}$...............(4)

From (3) and (4) we get,

$W.D=\int\ {k} \, dt = kt$

The work done by this force in time t is Kt.

So,option (C) is correct.