Question

A particle of mass m moves on a straight line with
its velocity varying with the distance travelled. If the
relation between velocity and distance is v = kx (K
is constant), then find the work done by the forces
during a displacement x = 0 to x = d.

Answer 1

Explanation:

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Answer 2

Answer:

Work done=$\frac{1}{2}mk^2d^2$

Explanation:

We are given that a  particle of mass m moves on  a straight line with its velocity varying with the distance traveled.

We are given that the relation between velocity and the distance is

v=kx where k is constant

Substitute x=0 then we get

v=0

Then , kinetic energy =k=$\frac{1}{2}mv^2=\frac{1}{2}m(0)=0$

Substitute x=d then we get

$v=kd$

Kinetic energy =$\frac{1}{2}m(kd)^2=\frac{1}{2}mk^2d^2$

Work done=Final kinetic energy- initial kinetic energy=$\frac{1}{2}mk^2d^2-0$

Work done=$\frac{1}{2}mk^2d^2$

Hence, the work done =$\frac{1}{2}mk^2d^2$