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The speed v reached by a car of mass m i...

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

A

`v=(3 xP)/(m)`

B

`v=((3xP)/(m))^(1//2)`

C

`v=((3xP)/(m))^(1//3)`

D

`v=((3xP)/(m))^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Power, `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)` or `v=((3xP)/(m))^(1//3)`.
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