Momentum

Momentum is a vector: when a ball bounces back or two objects approach, one velocity is negative relative to your chosen positive direction. Using $\Delta p = m(v + u)$ instead of $m(v - u)$ for a reversal gives an answer too large or of the wrong sign. Always define a positive direction first, then substitute signed velocities.

A change in momentum $\Delta p = m\Delta v$ has unit kg m/s (= N s) — that is the impulse, not the force. For the average force, divide by time: $F = \Delta p/\Delta t$ (unit N). "Rate of change of momentum" is the force, not the impulse, so it is wrong as an impulse definition. Never give an impulse in J.

A crash mat, airbag or rubber floor does NOT reduce the impulse — the impulse equals the change in momentum, fixed by the mass and speed. It extends the contact time, which reduces the average force by $F = \Delta p/\Delta t$. Write: same impulse, longer time, smaller force. "It cushions the impact" without the physics scores zero.

In an explosion the objects start at rest, so total momentum before = 0, and they push apart in opposite directions rather than stick together. In a collision where they stick, the combined mass moves off together. Do not add the masses for an explosion, and do not assume the objects stick unless the question says so.

Convert masses in grams to kg before using $p = mv$ — leaving 12 g as 12 gives a momentum 1000 times too large. Momentum has unit kg m/s (= N s), never J, and a bare number scores only part marks. Momentum is a vector, so state a direction wherever the question asks for one.