> Cars can stop in quite a short distance.

"Quite a short distance" is doing a lot of lifting. It's been a while since I've been to driver's school, but I remember them making a point of how long it could take to stop, and how your senses could trick you to the contrary. Especially at highway speeds.

I can personally recall a couple (fortunately low stakes) situations where I had to change lanes to avoid an obstacle that I was pretty certain I would hit if I had to stop.