A particle detector can be used to measure the speed of an unstable particle if the lifetime is known. Particle 'X' has mean lifetime \( \tau \) in its rest frame. Suppose 'X' particles are created in an experiment inside the detector by a nuclear reaction. If the 'X' particles leave tracks with mean length \( L \) before they decay into other particles, what is the mean speed of the 'X' particles? Express the answer in terms of the speed of light.\( \tau = 257.1 \, \text{ps}; \quad L = 11.3 \, \text{cm}; \)

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