A spaceship at rest in a certain reference frame S is given a speed increment of 0.50c. Relative to its new rest frame, it is then given a further 0.50c increment. This process is continued until its speed with respect to its original frame S exceeds 0.999c. How many increments does this process require?

Physics for Scientists and Engineers: Foundations and Connections
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Author:Katz, Debora M.
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Chapter39: Relativity
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Problem 39PQ: As measured in a laboratory reference frame, a linear accelerator ejects a proton with a speed of...
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A spaceship at rest in a certain reference frame S is given a
speed increment of 0.50c. Relative to its new rest frame, it is then
given a further 0.50c increment. This process is continued until its
speed with respect to its original frame S exceeds 0.999c. How
many increments does this process require?

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