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Fast pain or Acute Pain Happens In Response to an Event.
The nervous system quickly responds to a pain initiating event. Communication signals from the site of the event (say for example, you burn your hand while cooking) to the central processing unit (the brain) happen at speeds akin to 40 miles per hour. This is why, for example, you feel intense pain shortly after burning your hand. Because it results in your pulling your hand away from the source of heat, this is your nervous systems way of protecting you from further injury. The nerve fibers transmitting acute pain are myelinated, or covered with material that makes the messages move very fast.
Once the brain decides the event is not causing you any harm, it decreases the intensity of the communication signals associated with this singular event. In the case of the burned hand, after a while you may feel some discomfort, but the extreme pain is gone.
Resources - Chronic Back and Neck Pain