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Homework Help: Special relativity - A problem on velocity addition (several increments)

  1. Apr 4, 2012 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations
    Velocity addition formula
    (u + v)/(1 + uv/c^2)

    3. The attempt at a solution
    Speed after 1 increment = 0.50 c
    Speed after 2 increments = (0.50 + 0.50) * c/(1 + 0.50*0.50)
    = 0.80 c
    Speed after 3 increments = (0.80 + 0.50)*c/(1 + 0.80*0.50)
    = (13/14) c

    But problem is I do not know how long to continue like this. Is there a simpler approach? I am not able to find if there is a generic expression for the velocity after nth increment for any given value of n.
  2. jcsd
  3. Apr 4, 2012 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    You could try the stuff suggested by tom.stoer and DrGreg in this thread. See post #6.
    Last edited: Apr 4, 2012
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