Momentum Calculator

The momentum calculator evaluates the linear momentum of an object based on its mass and velocity.

Initial momentum28,000 kg·m/s1,400 kg × 20 m/s

Final momentum0 kg·m/s

Change in momentum (impulse)-28,000 kg·m/salso N·s — the two units are identical

Kinetic energy before280 kJ

Kinetic energy after0 J

Energy lost280 kJto deformation, heat and sound — momentum is conserved in a collision but kinetic energy is not

Average force186.6667 kN28,000 kg·m/s over 0.15 s

Force in g of deceleration13.6 g

If the stop took 2× as long93.3333 kN50% less force, for the same change in momentum

If the stop took 5× as long37.3333 kN80% less force, for the same change in momentum

Stopping distance at constant force1.5 m

The formula

p = mv; impulse = FΔt = Δp

Impulse is why crumple zones work

Momentum is mass times velocity, and the impulse — force multiplied by the time it acts — equals the change in momentum. A car stopping from a given speed must shed a fixed amount of momentum whatever happens, so the only variable is how long the stop takes. Double the duration and the force halves.

That is the entire design principle behind crumple zones, airbags, crash mats and bending your knees when you land. None of them reduce the momentum you have to lose; they stretch the time over which you lose it, and force is what does the injuring.

Note the asymmetry between the two conservation laws. Momentum is conserved in every collision, always. Kinetic energy is conserved only in a perfectly elastic one, and a car crash is emphatically not that — the missing energy went into deforming metal, which is precisely what you want it to do.