A machine delivers power to a body which is proportional to velocity of the body. If the body starts with a velocity which is almost negligible, then the distance covered by the body is proportional to

Options

A. (a) `sqrtv`
B. (b) `root3(v/2)`
C. (c) `v^(5//3)`
D. (d) `v^2`

Answer

D

Explanation

`Power=Fvpropv`
`=mv(dv)/(dt)=kv`, where `k=const ant`
`impliesm (dv)/(dt)=kimpliesmv(dv)/(dx)=k`
`impliesvdv=k/mdx`
Integrating both sides, we get `v^2/2=k/mx`
Hence, displacement is proportional to the square of instantaneous velocity.