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Time dilation equation

  1. Dec 17, 2011 #1
    A moving clock is observed to run four times more slowly than an identical
    stationary clock. What is its speed relative to the frame of the stationary clock?

    I'm wondering which equation should I be using for this?

  2. jcsd
  3. Dec 17, 2011 #2


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    What equations do you know of that might be relevant here?
    Which of the quantities in those equations are given (and what is the one you want to calculate)?
  4. Dec 17, 2011 #3
    I've been using

    t = t0 / sqrt(1 - v^2/c^2)

    t = 4t / (1 - v^2/c^2)^0.5

    (1 - v^2/c^2)^0.5 = 4t/t

    1 - v^2/c^2 =16

    -15c^2 = v^2

    v = (-15c^2)^0.5
  5. Dec 17, 2011 #4
    This is what i think it is:

    delta t' = delta t/sqrt(1-(v/c)^2)

    delta t = proper time, time interval in moving frame as measured by the moving frame
    delta t' = time interval of moving frame as measured by rest frame.

    So delta t' = 4 delta t, as the time interval of the moving clock is measured 4 times slower than stationary clock.

    Therefore 4 = 1/sqrt(1-(v/c)^2)

    Then you should be able to solve and find v as a fraction of c.
  6. Dec 17, 2011 #5
    Thank you.

    I'm now getting answer of ((15/16)^0.5)c
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