A particle is at rest at `x=a`. A force `vecF=(b)/(x^(2))veci` begins to act on the particle. The particle starts its motion, towards the origin, along X - axis. Find the velocity of the particle, when it reaches a distance x from the origin.

Explanation

`F=-(b)/(x^(2)) rArr (d)/(dt)(p) =-(b)/(x^(2))`
`(d)/(dt)(mv)=-(b)/(x^(2)) rArr m(dv)/(dx)(dx)/(dt)=-(b)/(x^(2))`
`mvdv=-(b)/(x^(2))dx rArr vdv=-(b)/(mx^(2))dx`
`int_(0)^(v)vdv=int_(a)^(x)-(b)/(mx^(2))dx rArr (v^(2))/(2)=(b)/(m)[(1)/(x)]_(a)^(x)`
`(v^(2))/(2)=(b)/(m)[(1)/(x)-(1)/(a)]" "therefore v=sqrt((2b)/(m)((a-x)/(xa)))`