Double the Speed: Momentum Doubles, Energy Quadruples

One of the two is conserved in a collision

Momentum is conserved whatever happens: add up the momentum of everything before a collision and after it and the totals match, whether the vehicles bounce apart or weld themselves together. Kinetic energy is not — in almost every real impact a large part of it disappears from the motion and reappears as bent metal, heat and noise. That difference is the entire design brief of a crumple zone: the momentum has to go somewhere regardless, so the structure is built to spend the energy on deforming itself over as long a distance as possible rather than on the occupants over a short one.

Mass and speed are not interchangeable

For momentum they are: a 3,000 kg vehicle at 14 m/s and a 1,500 kg one at 28 both carry 42,000 kg·m/s, and a collision between either and a wall lasting the same time needs the same force. For energy they are not — the heavier slower one carries 294,000 joules against the lighter faster one's 588,000, twice as much for the same momentum. This is why speed limits do more for safety than weight limits, and why a light vehicle travelling fast is a different problem from a heavy one travelling slowly even when the two look identical on one of the two measures.

Frequently asked questions

Does momentum have a direction?

Yes, and that is what makes it conserved in the useful way. Two identical cars meeting head-on at the same speed carry equal and opposite momentum, so the total is zero before the impact and zero after it — which is exactly why both end up stationary. Energy has no direction and cannot cancel like that: the two cars' kinetic energies add rather than subtract, and all of it has to go into deformation. That asymmetry is why a head-on collision between two vehicles at 50 is far worse than one vehicle hitting a parked one at 100 would suggest by momentum alone.

What are the units telling me?

Kilogram-metres per second is also newton-seconds, and the second reading is the more useful one: it says momentum is a force multiplied by a time. Stopping 21,000 kg·m/s in one second takes 21,000 newtons; stopping it in a tenth of a second takes ten times that. Extending the duration of an impact is therefore the only lever available once the momentum is fixed, and it is what an airbag, a crash barrier and a climbing rope all do — none of them reduces the momentum, all of them spread it over more time.