Comment by firebot

Because it's not momentum. ;p

F=ma (Force equals mass times acceleration)

W=Fd (work equals force multiplied by distance)

V^2=2ad (velocity squared equals two times acceleration times distance)

So W = Fd = ma(v^2/2a)

Finally: W=1/2mv^2 (work equals 1/2 mass times velocity squared)

So this explains why car crashes can be so dramatic, as a doubling of speed results in 4x the kinetic energy.