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OK--then help me out here, for my gen-ed students and in fact myself.
Low
velocity momentum is mass x velocity.
We know the velocity of a an object
is limited by 'c'.
The momentum of a fast object increases faster than the
velocity.
Is there really any 'conceptual' way to view this other than that
the mass has effectively increased.
Saying just that the momentum increases
non-linearly may be the most 'correct' thing to say, but not very
satisfying.
I know JD will say use time-space diagrams