To add onto the sibling's point, the "safe following distance" has a rule of thumb of "3 seconds behind". At 65MPH, I'm assuming you're in the US, is approximately 300 feet.

I'm willing to bet that's around 10 times what you were considering as a safe following distance in your head, and probably still 5 times more than what you were picturing for the safe distance behind a brake checking AV.