# Linear acceleration and speed of light and pions

## Homework Statement

In a particle physics experiment a particle called pion is used to hit a target. The particle pion has a (rest) lifetime of 2.6x 10-8 second and is accelerated to a speed 0.99c with respect to the linear accelerator. A straight beam pipe is used to transport the pions to the target. What would be the maximum length of the beam pipe? What is the length of the beam pipe the pions see?

## Homework Equations

Relativistic formulas..
To an observer at rest, the clock in a moving system appears to have slowed down, so that time intervals seem longer than his own clock intervals (time dilation).

[delta]t = [delta]t’/√ (1 - v^2 / c^2 )

Similarly, to an observer at rest the meter stick of the moving system appears shorter than his own meter stick (length contraction)

L = L’ *√ (1 - v^2 / c^2 )

## The Attempt at a Solution

I tried to put in the numbers given and put them in the formulas but I'm not completely sure what I should do. Any help is appreciated.

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Please write out your work so far so we can help better. Otherwise we have no idea where you got stuck.

Well I put in 2.6x 10-8 for velocity. But I have no idea what I am supposed to do. I missed the last week of class and need help with this problem. I don't think that is the right thing to do.

2.6E-8 sec is the time that it takes for the pion to decay in its rest frame. It is not a velocity. The velocity would be 0.99c where 'c' is the speed of light.

2.6E-8 sec is the time that it takes for the pion to decay in its rest frame. It is not a velocity. The velocity would be 0.99c where 'c' is the speed of light.
So I put .99c in for the v's. I still don't know how to get the answer still I'm lost, but thanks for your help.

Unfortunately this isn't the best place to teach the whole subject. Here are some good sources:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html" [Broken] (Check the Time Dilation section)

http://www2.slac.stanford.edu/vvc/theory/relativity.html" [Broken] (Read time dilation for particles section and the rest of it)

If you have more questions then just ask.

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