To other replies, since we've reached max depth: yes, and that's why it makes no sense to me to equip such badly-spec'd vehicles with the self-driving bits first (Tesla S excluded). I drive a higher-than-normal performance vehicle for the exact reason that it gives me more options when I need to get out of a bad situation. I can out-break, out-swerve (more lateral grip), and out-accelerate most other cars on the road. The stopping distance (factor of tire grip and break power) has definitely helped me avoid accidents. Lower body roll = more grip during more extreme maneuvers + more control during them.

Top Gear discussed speed limits being set based on worst-case breaking distances. Here's an analysis of that: http://www.jmp.co.uk/forward-thinking/update/top-gear-and-sp... but TL;DR performance vehicles can be safer since they're more capable.

Think what an F1 or rally car could do with computers driving it and avoiding accidents.

Still would be nice if the software could go "shit I'm about to get into an accident" and deploy air bags etc. that much faster. Plus now that I'm thinking about it, most accidents probably occur with some option that, had it been utilized, would've prevented the incident. Imagine the insane accident-avoiding swerve maneuvers a software program could potentially pull off.

> It's not quite possible to write a car that avoids ALL accidents because a car has a speed and a turning radius and breaks only work so fast.

It's not possible to have a self-driving car avoid all accidents, but one can presumably get pretty close. The realtime data from sensors give you enough information about the car itself, its surroundings and other objects around it to continuously compute a safety envelope - a subspace of the phase space of controllable parameters (like input, steering) within which the car can stop safely - and then make one of the goals to aggressively steer the car to remain in that envelope. This approach should be able to automagically handle things like safe driving distances or pedestrians suddenly running into the street.

Of course there will be a lot of details to account for when implementing this software, but it's important to realize that we have enough computing power to let the car continuously have every possible backup plan for almost any contingency in its electronic brain.