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

Explanation

`F prop x^(-1//4)`
`rArr a prop x^(-1//4)`
`rArr a=kx^(-1//4)" (where k is a proportionality constant)"`
`a=(dv)/(dt)=(dx)/(dt)(dv)/(dx)=kx^(-1//4)`
`(vdv)/(dx)=kx^(-1//4)dx`
`in vdv=kintxx^(-1//4)dx`
`int vdv=kintx^(-1//4)dx`.
`(v^(2))/(2)=k(x^(3//4))/(3//4)`
`v^(2) prop x^(3//4)`
`v prop x^(3//8)`
`therefore P=Fv`
`P prop (v^(3//8))/(x^(1//4))`
`P prop x^(1//8)`