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

Hint : `F prop x^(-1//2)" "therefore a=kx^(-1//2)`
`a or (vdv)/(dx)=kx^(-1//2)`
`intvdv=kintx^(-1//2)dx`
Find v.
`P=Fv`
`P prop (v)/(sqrtx)`
`F prop x^(-1//2)`
`a prop x^(-1//2)`
`a=kx^(-1//2)" (k is a proportionality 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) prop x^(1//2)`
`v prop x^(1//4)`
`P=Fv`
`P prop (x^(1//4))/(sqrtx)`
`P prop x^(-1//4)`