The total system energy is not a useful parameter in analyzing
this problem. Stating that the total system energy is conserved
is what one calls a trivial statement in that context.
Brian's analysis neglects my stipulation that in the collision
between the moving and stationary cars the stationary car must
have its brakes off. Immediately after the collision the two
cars are moving with the initial momentum of the first car.
In the ensuing interval the two cars must come to rest by
dragging debris in contact with the roadway; in that way the
two collisions are inequivalent. That is why I stated that the
hypothetical system I constructed was "The nearest equivalence
I can think of".
It is silly and not very physical to try to take such things as
this "shock" ad seriously. These are made by the relatively
ignorant for consumption by the relatively ignorant. Henry
Kuhlman was quite right in protesting the unphysical hyperbole
in this particular ad, however. It would, perhaps, make an even
greater impression on Joe Sixpack if the car were said to hit a
tree at three hundred miles per hour, but credulity, too, has
an elastic limit!
Why do I not hear you physicists protesting about something
much more important that is within your competence to protest?
I refer to the raucous and potentially very socially expensive
hyperbole with regard to anthropogenic global warming? Is that
not much more scientifically important than false advertising?