I was reading one of the recent questions involving a fast-moving superhero, and it reminded me of something I've been wondering about for a while, so I decide to create a spinoff scenario question.
Speedster Bob is a superhero, so he likes rescuing people. Damsel Jane is being threatened by Jerkface Joe, who is holding a standard handgun. Joe decides to point his gun at Jane. He isn't planning on shooting her, yet, just pointing it, but Bob doesn't know this. Bob doesn't want to allow this, because he doesn't want Jane shot. Bob is standing approximately 15 feet away from Joe, who is aware of his presence but currently focused on Jane.
Given this scenario, these things need to occur to achieve Bob's goal of preventing Jane's death (or injury). 1) he needs to recognize Joe's intended movement and 2) he needs to cross the space between them and grab/push Joe's arm before Joe can recognize he has begun to move, change his intention from simply pointing to shooting Jane, finish his initial motion, and pull the trigger.
Now, for an average human, this is extremely risky. You'd be more likely to get yourself shot (no matter what the movies say), and have to be super lucky to pull it off. But Bob isn't super lucky, just super. So he is pretty sure he can pull it off with a relatively high chance of success.
Assuming that Bob's top speed is not limited, then I think it comes down to his reaction time and rate of acceleration from a stopped position.
If Joe's reaction time is that of an average healthy adult, what are the minimum estimates of what Bob's super reaction time and acceleration would need to be in order to successfully pull off this move?