The velocity of the system's center of mass.

$$v_{cm} = \frac{\sum \vec{p}}{\sum m}$$ where $\sum \vec{p}$ is the sum of all individual object momenta and $\sum m$ is the total mass of the system.

Sum of all individual momenta in a system.

Impulse ($j$) is the change in momentum ($\Delta p$) of a system: $$j = \Delta p$$

Any change in momentum for one object is balanced by an equal and opposite change in momentum for another object (Newton's Third Law).

Impulse is equal to the change in momentum: $$j = \Delta p$$

The change in momentum of the system will equal the impulse of that force.

The total momentum of that system stays constant.

Impulse causes a change in momentum.

The total momentum of the system changes; momentum is transferred between the system and its surroundings.

Momentum is transferred between the objects such that the total momentum of the system remains constant.

The object's momentum changes by an amount equal to the impulse: $\vec{J} = \Delta \vec{p}$

The total momentum of the system remains zero (if it was initially at rest), with the individual components moving in opposite directions to conserve momentum.

The collision is classified as elastic.