Paper 4, Section II, B

Dynamics and Relativity | Part IA, 2010

Let SS be an inertial frame with coordinates (t,x)(t, x) in two-dimensional spacetime. Write down the Lorentz transformation giving the coordinates (t,x)\left(t^{\prime}, x^{\prime}\right) in a second inertial frame SS^{\prime} moving with velocity vv relative to SS. If a particle has constant velocity uu in SS, find its velocity uu^{\prime} in SS^{\prime}. Given that u<c|u|<c and v<c|v|<c, show that u<c\left|u^{\prime}\right|<c.

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