The response time of adrenaline is almost instantaneous. When you are confronted by a danger or fear, then a part of your brain called the amygdala is activated. The amygdala then activates the fight or flight response, which results in the release of adrenaline into the bloodstream, which then prepares the the body to either fight or run from the danger. So the time from when you sense the danger to when adrenaline is released is almost instantaneous.