The velocity of a moving body of mass m along positive.x axis is v`=a sqrt(x)` (a=constant). Find the work done by the force applied on the body to displace it from x=0 to x=l.

Explanation

Power , P =Fv =mfv=mv `(dv)/(dt)`
[ acceleration of the body =`(dv)/(dt)`] So, work done,
`W=int pdt m=int vdv =(mv^2)/(2)+c=(ma^2x)/(2)+c`
[c= integration constant ]
At x=0 , W=0 `therefore c=0`
Now when `x=l , W=1/2 ma^2l`