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Smriti Sabharwal
Asked: 2022-11-04T23:02:29+05:30 In:

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

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

  1. Correct Answer – C
    `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)`

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