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Technically speaking yes it can, because the definition of air force one is any air force plane that the president is in so for an example if a president decides to fly in an Air Force fighter jet like the F-15 his call sign would be air force one and it could break the sound barrier, but traditionally speaking the plane he flies daily can not break the sound barrier.

The VC-25 (Boeing 747) the President typically flies is not supersonic within its normal flight envelope. That being said, a DC-8 once did break the sound barrier in a shallow dive as part of a controlled test, so it is theoretically possible for commercial airliners to break Mach 1, but strictly speaking a 747 is not a supersonic aircraft.

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