I stumbled across this bear attack story from Alaska that was pretty hair raising.  This guy showed unbelievable fortitude in not shooting until he did.  Just so it's clear what they are talking about, brown bears are what they call grizzlies up in Alaska.  Notice their amazement at the speed of these giant predators as well.  From what they describe, there is simply zero chance of outrunning a determined bear.  Worth the read, indeed.