# Calculating lifetime of a moving pion

1. Nov 12, 2008

### crh

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

$$\Delta t$$ = $$\Delta t0$$ / $$\sqrt{1-(v2/c2}$$

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.
$$\Delta t$$=4.91E-8s
$$\Delta t0$$=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. Nov 12, 2008

### CompuChip

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

You have $\Delta t$ and $\Delta t_0[/tex], so basically it comes down to applying your math skills to solve for v. [Hint: let [itex]\beta = v / c$ 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 $x = \sqrt{1 - \beta^2}$ and solve for x first.]