a body is moved along a straight line by a machine delivering constant power .The distance moved by

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Discussion Response Post to: a body is moved along a straight line by a machine delivering constant power .The distance moved by

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Soumen Goswami (2446)

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Given
P = k (a constant)
Fv = k
m(dv/dt)v = k
m(dv/dx)(dx/dt)v = k
mv²(dv/dx) = k
m₀^v v²dv = k₀^x dx
mv³/3 = kx
v = (3kx/m)^1/3
v x^1/3

Let v = ax^1/3, where a is a constant. Then,

₀^x x^-1/3 dx = a ₀^t dt

(3/2)x^2/3=at

x t^3/2

There's a little problem in the solution provided by Badran. The solution assumes constant acceleration. Constant power doesn't necessarily imply constant acceleration.

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