It can't detect when a crash is about to happen. The driver manually pushes the brakes there.

I have only worked tangentially with self-driving systems but in general they are very bad at dealing with stationary objects - this is why it can't see the center barrier.

This article describes the reason why radar and stationary objects don't mix: https://www.wired.com/story/tesla-autopilot-why-crash-radar/

How far ahead can LiDAR detect stationary objects? Will there be enough time on a highway to brake or steer away from suddenly appearing obstacles?

The latest Waymo video [1] says its car can see up to 3 football fields away. I would guess this would let it operate at higher speeds. I haven't seen any demos of it on the highway. I think they're focused on cities and suburbs.

[1] https://youtu.be/B8R148hFxPw?t=1m28s

Ok. Can it see potentially dangerous obstacles that stick out of the ground by, say, 10 inches?

It can see ducks..

https://www.youtube.com/watch?t=26m15s&v=Uj-rK8V-rik

> I don't understand how the Tesla couldn't see the centre barrier but it can detect when a crash is about it happen, can someone explain that?

AFAIK the AP focuses more on moving targets for collision avoidance, stationary objects are harder because there's so many of them you'll never hit since they're above or next to the road, but that's hard to tell until they're very close (can't see where the road leads to 100m away).

That's the very definition of "you're driving way too fast (and if that's your only detection method, you shouldn't be on the road)".