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. (a) `v=(3xP)/(m)`
B. (b) `v=((3xP)/(m))^(1//2)`
C. (c) `v=((3xP)/(m))^(1//3)`
D. (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^2dv=P/mdx`
On integration, we get `v^3/3=(Px)/(m)` or `v=((3xP)/(m))^(1//3)`