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In one of Massad Ayoob's books, he mentioned having all sorts of people do this drill in his classes playing both sides. He said some athletic people can cover that distance in less than 1 second, but even apparently slow or impaired people can cover it faster than you think.

The first thing that jumps to mind is seeing the cops continue to try to draw from a retention holster while the attacker closes the final few feet. After that, even if they managed to draw and fire, the person might not stop and can likely still do plenty of damage.