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. `sqrt(v)`
B. `3sqrt((v)/(2))`
C. `v^(5//3)`
D. `v^(2)`

Explanation

Power `=Fv=m(dv)/(dt)(v)alphav`
`rArr mv(dv)/(dt)=k_(0)v`, where `k_(0)=` constant
`rArrm(dv)/(dt)=k_(0)rArrmv(dv)/(dx)=k_(0)`
`rArr vdv=(k_(0))/(m)dx`
`rArr` integrating both sides,
`int_(0)^(v)vdv=(k_(0))/(m)int_(0)^(x)dx`
`(v^(2))/(2)=(k_(0))/(m)x`
Hence, displacement is proportional to square of instantaneous velocity.