[HPsquared]

Although the single car at 100 MPH has twice the initial kinetic energy of two cars at 50 MPH, not all of this gets dissipated in the collision. After the collision in the "single car 100 mph hitting an identical stationary car" case, we have both cars moving at 50 MPH in the same direction, NOT two stationary cars. Half the original kinetic energy is still in the form of kinetic energy, in other words. The 100MPH car does not experience a velocity change of 100 MPH, but only 50 MPH - the same as if it had hit an oncoming car at 50MPH.