Earlier quoted context omitted.
In a multi-car pileup, the car immediately in front of you literally stops in an instant, much faster than if it were to fully hit the brakes. It's much faster than any driver could realistically expect. It can happen so fast, you may not even see brake lights turn on. It's why these pileups can get so surprisingly large.
Just to quantify this, the shortest 60-0 stopping distance for a "consumer-grade" car (meaning not a formula one vehicle) is the Porsche 911, which can do it in 27m. This is nearly 6 vehicle lengths. Usual safety guidelines are to stay about 3 car lengths behind whoever you're following, so even world's greatest brakes are not gonna save you if the vehicle in front stops in 0m because it hits an immovable pile of alr…
No, safety guidelines are to follow 3 SECONDS behind the car in front, which is about 100m at 70mph.