This is why you never tailgate cars on bikes.
You cannot stop faster as physics rule, the car has more mass, more rubber on the ground so it can scrub speed faster than a smaller lighter vehicle with two small patches of grip. You can also only react after you see the lights meaning your behind the eightball already.
On a rider training course they hired a Toyota Corolla and made us do emergency braking tests from 30mph to stop, there were a range of bikes, speed triples, FJ's, ST's, BMW's etc, the car virtually stopped in half the distance of the best bike/rider combo. We then said "ah ha what if the cars loaded with people? So as many people as possible were crammed in, car stopped in same distance. I stopped one of my bad habits that day.
Best to leave the cages a bit of space or at least make sure you can veer around them