Applying the Law of Conservation of Momentum

Train car A is at rest when it is hit by train car B. The two cars, which have the same mass, are stuck together and

move off after the collision. How does the final velocity of train cars A and B after the collision compare to the initial

velocity of train car B before the collision?

The final velocity is double train car B's initial velocity

The final velocity is the same as train car B's initial velocity

The final velocity is half of train car B's initial velocity

The final velocity is zero since train car B will stop.

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