Momentum is a quantity that is conserved. This means that the total amount is constant throughout an interaction, such as a collision, provided that there are no external forces acting.
Since velocity is a vector quantity, so too is momentum, and so momenum in the reverse direction will be negative.
Key Concepts
By applying Newton's three laws to a collision between two balls, we can show that the total momentum for isolated bodies is constant. Momentum is conserved.
Essentials
Elastic collisions
Identical bodies
An elastic collision means that total kinetic energy is constant. Recall that kinetic energy is a scalar (since the velocity term is squared) and so energies are added together no matter what the direction.
When two identical balls collide elastically they swap velocity, so if one was stationary before the other will be stationary after.
Non-identical bodies
The momentum before a collision always equals the momentum after, provided the bodies are isolated.
Explosions
There is no momentum before an explosion. After the explosion, the bodies have velocities in different directions.
If the system is isolated, the momentum is conserved. Therefore, the bits going left are balanced by the bits going right (and the same could be said up and down).
2-dimensional collisions
Momentum is conserved in 2-dimensions. To show this we can either make a triangle of the vectors or take components.