# 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?

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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 vafter​:

mv=4mvafter

cancelling out the m's:

v=4vafter

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

vafter​=0.25v