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Homework Help: Calculating lifetime of a moving pion

  1. Nov 12, 2008 #1


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    1. The problem statement, all variables and given/known data

    What is the speed of a pion if its average lifetime is measured to be 4.91E-8s? At rest, its average lifetime is 2.60E-6s. What is the particle's lifetime at rest?

    2. Relevant equations

    [tex]\Delta t[/tex] = [tex]\Delta t0[/tex] / [tex]\sqrt{1-(v2/c2}[/tex]

    3. The attempt at a solution

    I don't want to type in all the numbers in the equation so I will tell you where they go.
    [tex]\Delta t[/tex]=4.91E-8s
    [tex]\Delta t0[/tex]=2.60E-8s

    I have everything plugged into where it needs to go, I just can't derive the answer. I am needing to find "v" in terms of "c", if that makes sense. My answer will be v= #.##c
    Can someone help me.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Nov 12, 2008 #2


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    Science Advisor
    Homework Helper

    Well, you have the relation
    [tex]\Delta t = \Delta t_0 / \sqrt{1 - v^2 / c^2}[/tex]
    (click that to see the LaTeX code by the way, you'll see it's much easier than and :smile:)

    You have [itex]\Delta t[/itex] and [itex]\Delta t_0[/tex], so basically it comes down to applying your math skills to solve for v.

    [Hint: let [itex]\beta = v / c[/itex] and solve for beta, that will give you the velocity already expressed in c ].

    [Second hint: If you don't see how to solve the equation right away, let [itex] x = \sqrt{1 - \beta^2}[/itex] and solve for x first.]
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