I have a physics question
 

I saw this on an episode of Archer this morning and it got me thinking.

Car A is moving forward at x speed (idk that the speed maters)
Car A losses its brakes and can't stop

Car B does a 180 and aligns Hood to Hood with Car A.

What is the fastest way for Car B to stop Car A?

My guess is that accelerating through Car A would stop the car faster than applying the brakes.

Ignore all variables such as steering, alignment, fish tailing road surface. (unless any of these would actually play a huge role on getting the answer)

The coefficient of friction of the tires is the limiting factor. If the car's brakes are strong enough to lock or engage ABS, the the brakes will apply the maximum possible force.