OK then lets look at the conservation of energy angle then:
Car A = E1
Car B = E2
E1 = E2
Combined energy is E1 + E2, in a head on the kinetic energy is shared equally between the two.
When Car A hits the immovable wall, energy will still be imparted into the wall as heat, sound waves, etc. The energy acting on the car must be less.
Chopped, did you never play conkers ? The balls not got thud and stop.
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