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A machine delivers power to a body which...

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

A

`sqrt(v)`

B

`root(3)(V/2)`

C

`v^(5//3)`

D

`v^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Power `=Fv=m (dv)/(dt)(v) prop v`
`rArr m v(dv)/(dt)=k_(0)v" "` where `k_(0)=` constant
`rArr m (dv)/(dt)=k_(0)`
`rArr mv(dv)/(dx)=k_(0)`
`rArr vdv=(k_(0))/(m)dx`
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 instanfaneous velocity.
Hence (D) is correct.
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