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.

A particle is at rest at x=a. A force vecF=(b)/(x^(2))veci begins to a

1.	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.
Answer» SOLUTION :`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)))`