The classical equation for momentum (p=mv), frustratingly enough, becomes inaccurate when velocity approaches the speed of light—that is, momentum increases exponentially with increased velocity. The formula for relativistic momentum is:


where c is the speed of light. So, a physics textbook with a mass of 5 kg moving at .95c would, under Newtonian physics, have a momentum of 1,425,000 kg·m/s (the unit for momentum), but with this newfangled theory of relativity, its momentum is 4,563,652 kg·m/s-- more than three times as much! As velocity approaches c, the denominator of the fraction approaches 0, so the momentum approaches infinity—further proof that going faster than light is impossible, as it would require infinite force to produce an infinite change in momentum.

Note also that at everyday velocities, like 30 m/s, the denominator is so close to 1 (in this case, it's something like 1 minus 6.6x10-15) that it's virtually identical to the Newtonian model. Only at relativistic velocities is this model required.