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To simplify the discussion (somewhat) let's change the comparison to a
collision between two moving cars and one moving car and one parked car.
Now certainly a collision with the parked car at speed v is less serious
than a head-on with both cars travelling at v. In Michael's analysis below,
the assumption of equal times to come to rest is, I believe, the problem.
In the head-on, t will be smaller (assuming the center of mass will not move
once the cars make contact) than in the collision with the parked car (even
if that car doesn't move).