Two railway trucks of masses m and 3m move towards each other in opposite directions with speeds 2v and v respectively. These trucks collide and stick together. What is the speed of the trucks after the collision?

In order to solve this question we need to use the principle of conservation of momentum which states:

The momentum in a closed system remains constant before and after a collision or explosion.

I.E.

momentum before=momentum after

And ingeneral momentum is calculated using: P=mv where P is the momentum, m is the mass of the object, and v is the velocity of the object.

Hence the total momentum before the collision is:

P1+P2

=m x 2v + 3m x -v       NOTE: notice the negative v on the second truck as it is moving in the opposite direction to the first truck

=-mv

After the collision the the trucks stick together so the total mass becomes 4m and the combined trucks move at an unknown speed of v_​after

We will solve the equation for conservation of momentum to determine v_after​:

mv=4mv_after

cancelling out the m's:

v=4v_after

and rearranging to make v_​after the subject of the equation:

v_after​=0.25v

Which is our final answer.