answer
the final velocity is half of train car B's initial velocity
explanation
the conservation of momentum states that the initial and final total momentum are equal
m1v1 + m2v2 for initial momentum
(m1 + m2)v3 for final momentum because both cars stick together so their masses are combined
m1v1 + m2v2 = (m1 + m2)v3
since the mass of both are the same, m1 = m2
m1v1 + m1v2 = (m1 + m1)v3
m1(v1 + v2) = 2m1v3
divide both sides by m1
v1 + v2 = 2v3
since train car A is initially at rest, v1 = 0
v2 = 2v3
v3 = v2 * 1/2
the final velocity is half of train car B's initial velocity
