What are pre collision and post collision exactly? I assume it is before collision and after collision. I can not find an answer on google.
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Yes, it is exactly that. Because collisions are impulsive, the effects of a collision cannot be handled by the usual implementation of Newton's second law relating force to mass and acceleration.
So instead, the conservation laws are written down, relating the momenta (and kinetic energies) before and after the collision to the impulse (force integrated over the very short time of the collision). Usually, in order to completely solve the dynamical problem, an extra condition needs to be imposed: for example, that the colliding surfaces are smooth, and hence the impulse acts perpendicular to them, at the point of impact.