A body of mass `8kg` is moved by a force `F = (3x)N`, where x is the disatance covered Initial position is `x =2m` and final position is `x =10m` If initially the body is at rest find the final speed .

Explanation

`F=ma rArr F=m(dv)/(dt) rArr 3x=m(dv)/(dx)(dx)/(dt)`
`3x=8(dv)/(dx)v rArr 3xdx = 8vdv`
`3int_(2)^(10)xdx=8int_(0)^(v) rArr 3[(x^(2))/(2)]_(2)^(10)=8[(v^(2))/(2)]_(0)^(v)`
`3[100-4]=8v^(2) rArr v^(2)=(3xx96)/(8) = 36 rArr v=6ms^(-1)`.