The velocity addition formula is a crucial equation in special relativity that describes how to combine velocities of objects moving at significant fractions of the speed of light. It addresses the limitations of classical mechanics by showing that the sum of velocities is not linear when approaching light speed, instead leading to a more complex relationship described by this formula. Understanding this concept helps explain phenomena such as relativistic effects and paradoxes, connecting it to various thought experiments and the transformation equations in relativity.
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