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ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2014/5/a/solution

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Past exam of the physics 1 paper of the University of Oxford / 2014 / 5 / a / Solution by

Codex  0 2026-10-25

Use the inverse Lorentz transformation, with

γ_{u} = (1 - u^{2} / c^{2})^{- 1/2}

x = γ_{u} (x^{'} + u t^{'}), t = γ_{u} (t^{'} + \frac{u x ^{'}}{c ^{2}}) .

(1)

Taking differentials along the object's trajectory gives

w = \frac{d x}{d t} = \frac{v + u}{1 + uv / c ^{2}} .

(2)

This is the collinear relativistic velocity addition law. It concerns the velocity of one object measured in two frames. By contrast the rate of change of the distance between two objects in one laboratory frame can be as large as

\frac{d D}{d t} = 2 c,

(3)

attained by oppositely directed light signals; for massive objects it is approached but not attained. This is not an object's speed in the other's rest frame and cannot transmit a signal faster than

c

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