Great question! These are the fun questions to think about.
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From what I understand, the mass of an object does not actually change with speed. The (kinetic) energy increases with increased speed. This article has a good explanation: http://wtamu.edu/~cbaird/sq/2013/06/18/can-you-go-fast-enough-to-get-enough-mass-to-become-a-black-hole/
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I think the reason why people think more speed equals more mass is because they forget about relativity. Physics still applies in all reference frames regardless of the speed.
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