Is two cars colliding at 25 mph the same as one car colliding into a wall at 50 mph in reference to injuries?

This question has been asked using 50 & 100 mph reference, see this Phys.SE post and links therein. However, I am interested in the potential injuries to occupants of the autos. As the one going into the wall has occupants going 50 miles per hour. The 2 cars have occupants in each car only going 25 mph at time of crash. Would the occupants of the 2 cars not have as much damage as the car with the wall as the 2 cars would decelerate based on the crushing of the cars. Knowing that the 2 cars would be absorbing the energy more than the 1 into the wall at 50 mph.

• It seems you answered your own question. Cars absorb energy better than a car + wall. – user6972 Nov 24 '13 at 5:06

Severity of injury is going to be proportional to the rate of change of momentum. Two cars colliding head-on will have a lower value of rate of change of momentum than one car striking a typical wall. Reason: a typical wall will not cushion an impact as well as a typical car.

More cushioning means the actual collision will take place over a longer time span. Time taken is higher and rate of change of velocity lower.

• The sort of walls that cars typically collide with in my locale are considerably more cushioning than an oppositely moving vehicle. I've seen several typical brick walls demolished by cars with relatively little damage to the car or occupants. – RedGrittyBrick Jun 9 '15 at 8:58

For each case think about the total kinetic energy and number of cars that are available to absorb all of it during impact and it should be apparent which case has more energy (damage) per car. (crushing, deformation, sounds are evidence of energy conversion, so a tough rigid wall doesn't absorb any)

A more challenging problem to intuition is (A) two cars crashing head on at 25mph each vs (B) one car crashing into a wall at 25mph