A particle is moving along x-axis under the action of force, F which varies with its position as `F prop(1)/(4sqrtx).` Find the variation of power due to this fore with x.

Explanation

`Fpropx^(-1//2)thereforea=Kx^(-1//2)`
`a or (vdv)/(dx)=kx^(-1//2)` ltbr"gt `intvdv=kintx^(-1//2)dx`
Find v. `P=Fv`
`Pprop(v)/(sqrtx)`
`F propx^(1//2)`
`a prop^(-1//2)`
`a=kx^(-1//2)` (k is a proporationality constant)
`(dv)/(dt)=(dx)/(dt)(dv)/(dx)=kx^(-1//2)`
`v(dv)/(dx)=kx^(-1//2)`
`intvdv=kintx^(-1//2)dx`
`(v^(2))/(2)=k(x^(1//2))/(1//2)`
`v^(2)propx^(1//2)`
`v propx^(1//4)`
`P=Fv`
`Pprop(x^(1//4))/(sqrt4)`
`P propx^(-1//4)`