Physics equations give me a headache. Make that a double headache when trying to apply to a real situation.
Here’s a quote from the April 1991 edition of Consumer Reports:
‘NHTSA crashes cars into a fixed barrier at 35 mph. That’s equivalent to two cars of equal weight hitting each other head-on while each is traveling at 35 mph.’ (page 219 paragraph 2)
This seems to suggest the guys may have been wrong when they told the caller the damage to each car would be representative of twice the speed of each car.
I believe the only way to prove this out is to replicate this head-on crash test of two identical vehicles (MG TD’s may be perfect for this) and then crash a third similar vehicle into a wall at 35 mph. Better yet, crash a fourth similar car at 70 mph into a wall for further comparison.
From what I think I know about Newtonian mechanics, Consumer Reports was right about this. Think about it: If the force was doubled, we’d have the solution to all of our energy problems, and we know that ain’t going to happen.
Consider it just a typo. It all makes sense if we read, “NHTSA crashes cars into a fixed barrier at 70 mph.” I don’t know if NHTSA actually performed 70 mph crashes; there seems little point in doing so. But it corrects the text.
Newton’s Third Law states that “For every action, there is an equal and opposite reaction.” Applied to this situation, that means that the force applied by the car to the wall equals the force applied by the wall to the car.
F=ma (force equals mass times acceleration), and the acceleration (or in this case, deceleration) is very fast (versus slow, like plowing a car into a giant pillow) so the force is high. If the rate of deceleration is the same for the car-to-car impact as it is for the car-to-wall impact, the forces applied will be the same.
It helps being a Physics major. 
This seems to suggest the guys may have been wrong when they told the caller the damage to each car would be representative of twice the speed of each car.
Think of it this way. Each car has energy equal to its weight times its speed. A wall has zero energy to add. Since a wall is considered a solid object it also will not absorb any energy. (A pillow will absorb energy) so the car has to absorb all the energy. It does this buy bending and breaking parts. Two cars exact mirror images running into each other would result in the same situation. If they were not mirror images or hit exactly correctly then one might absorb more energy than the other. Even a part that breaks off a car will absorb some energy as it slows down skidding down the highway.
Normally your brakes absorb the energy of stopping your car, they do that primarially by heating up. That pillow I spoke of earlier will do the same thing. If you carefully measure it and then start punching it then measure the temperature again you will find it is warmer, having absorbed that energy.It is all semantics. The driver goes from 60 to zero in both cases. In real life it is usually much better to hit an object at rest since you can impart some energy to the object you hit and decrease your deacceleration. Remember, physics also says wider tires don’t increase traction. The devil is in the details!