That's usually the right answer, but you have to be careful. For instance, you say the car will break faster than a human could. But if it does, the human-driven car right behind it is in trouble.
Yes, you'd want to have some sort of sensors behind the car as well, so that if it's possible to avoid hitting the object and avoid being hit by the car that you would brake at that speed. If it's not possible, well, it's still an improvement over a human driver.