relativistic momentum

Momentum measures how much motion an object carries — roughly, how hard it is to stop. In Newton's world it is simply mass times velocity, p = m v. Relativity keeps this idea but corrects it for high speeds by inserting the Lorentz factor, so the true formula is p = gamma m v, where gamma = 1/sqrt(1 - v^2/c^2).

At everyday speeds gamma is almost exactly 1, so the relativistic formula and the schoolbook one agree to many decimal places. But as an object's speed climbs toward the speed of light, gamma shoots up without bound, and so does its momentum. The same shove that easily speeds up a slow object barely budges one already moving near light speed.

This runaway growth is the deep reason no object with mass can ever reach the speed of light. To get there you would have to give it infinite momentum, which would take infinite energy — something no finite push can supply. Think of accelerating a car that gets heavier to nudge the closer it approaches some wall it can never touch.