A body of mas 5 kg is placed at origin. A force starts acting on the body given by `vecF=(2+3x)hati` where x is the distance of body from origin in meters. Find the speed acquired by the body as it passes through `x=5m.`

Explanation

Here the only force acting is `vecF=(2+3x)hati.` So body starts moving along x-axis. By applying work-energy principle.
`W=intvecF.vec(dx)=DeltaK`
`impliesunderset(0)overset(5)int[(2+3xx)hati].(dxhati)=1/2xx5v^(2)-0`
`impliesunderset(0)overset(5)int(2+3x)dx=5/2v^(2)`
`implies[2x+(3x^(2))/(2)]_(0)^(5)=5/2v^(2)`
`implies[10+75/2]-[0]=5/2v^(2)`
`impliesv=sqrt(19)m//s`