Impulse (J = FΔt)

Impulse is force multiplied by how long that force acts, $J = F\,\Delta t$, and its whole significance is that it equals the change in momentum produced. That is not a separate law — it is Newton's second law in its original form. Newton wrote that force is the rate of change of momentum, $F = \Delta p/\Delta t$, and multiplying both sides by $\Delta t$ gives this. The units confirm it: a newton-second and a kilogram-metre per second are the same thing.

Here is the calculation that motivates every piece of passive safety equipment in a car. A 70 kg occupant travelling at 15 m/s must lose $p = 70 \times 15 = 1050$ kg·m/s of momentum in a frontal impact. That number is fixed by the crash; nothing can reduce it. If the body stops against a rigid dashboard in 0.1 s, the average force is $F = 1050/0.1 = 10\,500$ N. Stretch the same stop to 0.5 s using a crumple zone, a seatbelt that pays out under load, and an airbag, and the force falls to 2100 N. The impulse is identical in both cases. Only the time changed, and the time is the only variable an engineer gets to design.

The same trade-off is why you bend your knees on landing, why a boxer rolls with a punch, why gymnasts land on foam, and why a fall onto concrete is dangerous and the identical fall onto a mattress is not. In the other direction it is how rockets are specified: a model rocket motor's class is its total impulse in newton-seconds, because that is what determines the velocity change it can give a vehicle, regardless of whether it burns fiercely for a moment or gently for several seconds.

Impulse is a vector, and the sign flip on a bounce is the classic error. A 0.15 kg ball thrown at a wall at 20 m/s and rebounding at 20 m/s has not undergone a momentum change of zero, and not one of 3 kg·m/s either. Its momentum went from $+3$ to $-3$, a change of 6 kg·m/s — twice what stopping it dead would have required. A bouncing collision always demands more impulse than a catching one, which is why a bouncy object hits harder than a soft one of the same mass and speed. The second caution is that $F$ here is the average force over the contact. A real impact pulse is peaked, often two to three times the average at its maximum, so a component designed only against the average will be under-rated for the moment that actually breaks it.