(a) At what speed is the momentum of a particle twice as great as the result obtained from the nonrelativistic expression mv? Express your answer in terms of the speed of light. (b) A force is applied to a particle along its direction of motion. At what speed is the magnitude of force required to produce a given acceleration twice as great as the force required to produce the same acceleration when the particle is at rest? Express your answer in terms of the speed of light.

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(a) At what speed is the momentum of a particle twice as great
as the result obtained from the nonrelativistic expression mv? Express
your answer in terms of the speed of light. (b) A force is applied to a
particle along its direction of motion. At what speed is the magnitude of
force required to produce a given acceleration twice as great as the force
required to produce the same acceleration when the particle is at rest?
Express your answer in terms of the speed of light.

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