A particle of mass m is constrained to move along a straight line. A and B are two fixed points on the line at a separation of L. When the particle is at some point P, between A and B, it is acted upon by two forces
`vecF_(1)=((6mg)/(L))vecPA " and " vecF_(2)=((3mg)/(L))vecPB`
At time t=0, the particle is projected from A toward B with a speed of `sqrt(gL)`.
At what time 't' will the particle reach at B for the first time ?

Answer

`t=(2pi)/(3) sqrt((L)/(3g))`