Momentum, $p=mv$ . Newton’s second law can be written as: $\sum F=\frac{\Delta p}{\Delta t}$ Momentum is conserved in all isolated, closed systems. Elastic collisions are when kinetic energy is conserved.

Impulse, $J=\Delta p=F\Delta t$.

One-dimensional collisions

There is an important formula that is not described in the textbook. $V_A-V_B=-(V_A^{{}^{\prime }}-V_B^{{}^{\prime }})$ Proof of One Dimensional Collision