The speed v reached by a car of mass m in travelling a distance x, driven with constant power P, is given by

Options

A. `v=(3xP)/(m)`
B. `v=((3xP)/(m))^(1//2)`
C. `v=((3xP)/(m))^(1//3)`
D. `v=((3xP)/(m))^(2)`

Answer

C

Explanation

`P=Fv=m(dv)/(dt)v`
or `v(dv)/(dt)=(P)/(m)` or `v.(dv)/(dx).(dx)/(dt)=(P)/(m)`
or `v^(2)(dv)/(dx)=(P)/(m)` or `v^(2)dv=(P)/(m)dx`
On integration, we get
`(v^(3))/(3)=(Px)/(m)a` or `v=((3xP)/(m))^(1//3)`