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This Demonstration considers the composition of velocities in accordance with the special theory of relativity. Consider a system moving with velocity represented by the red arrow, with magnitude ... and direction ... , with respect to a stationary frame of reference. The red disk recapitulates this magnitude, which has an upper limit extending to the red circle, corresponding to the speed of light ... . The blue arrow represents a second velocity, which has a magnitude ... and direction ... , with respect to the moving frame of reference. The velocity with respect to the original stationary frame is then represented by ... . A compact formulation gives the components of ... parallel and perpendicular to ... : ... The gray arrow represents the vector ... .

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