Initially acceleration of B and A is same along the string which is given by
a=2mgsin30∘−mgsin30∘3m=g6
After 2 seconds, speed of both A and B is
VB=VA=g6×2=103 m/s
When B is caught for a moment and released again, speed of B becomes zero,while A is still having a speed 103m/s up the inclined due to which string will become slack. But A will decelerate and B will accelerate. Because of this the string will become tight again after A and B travel the same distance.
Let this time interval be t,
From, s=ut+12gt2
103×t−12gsin30∘×t2=12gsin30∘×t2
as t≠0, t=23sec
At this time speed of A is given by
v=103−g2×t=103−102×23=0