When is a police officer or law enforcement official allowed to use physical/deadly force? How far are they allowed to go?

Physcial or Deadly force is the force which a person uses, or that a person knows, or should know, would create a substantial risk of causing death or serious harm. The use of deadly/physical force is justified only under extreme cercomstances of necessity  and as a persons last resort, when all other means have failed and nothing else can be done. The "Use of deadly force" is often granted to police when the person is believed to be an immediate danger to people around them.
A police or law enforcment officer may use physical force, in the course of attempting to effect an arrest, or preventing or attempting to prevent the escape of a person who the officer reasonably believes to have committed a crime or offense. The officer may use the force to the extent he or she believes to be necessary to effect the arrest, or to prevent the escape. Officers my also use physical force in self-defense or to defend a third person.





Sources-
http://en.wikipedia.org/wiki/Deadly_force