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Proper Time, 4-Velocity and 3-Velocity Question

  1. Jan 26, 2017 #1
    1. The problem statement, all variables and given/known data
    In special relativity, a uni-formally accelerated spaceship is a spaceship whose engine is set at a constant emission rate. For a spaceship that maintains such uniform acceleration in the x-direction of some inertial frame S, the wordline is given by

    t(τ) = c/a × sinh(aτ/c)

    x(τ) = c^2/a × (cosh(aτ/c) -1)

    y(τ) = 0

    z(τ) = 0

    where τ is the proper time of an astronaut on the spaceship. Show that the 4-velocity in the co-ordinates (ct, x, y, z) is given by:

    u^μ = (cosh(aτ/c) , csinh(aτ/c) , 0 , 0)

    and hence show that the spaceship's 3-velocity is given by

    u = (ctanh(aτ/c), 0 , 0)

    So I'm completely lost in the question. If someone can direct me on how to approach this question. Possibly some equations that can help me solve this problem.
    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
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