# Decay question

1. Oct 7, 2005

### asdf1

for this question:
a certain particle has a lifetime of 1*10^8 sec when measured at rest. How far does it go before decaying if its speed is 0.99c when it is created?

my problem:
because the particle is decaying, then its speed should be changing...
then there's two variables in this problem!
any suggestions?

2. Oct 7, 2005

### Physics Monkey

The particle doesn't change its speed until it decays, why would it? This is a standard time dilation problem I think.

Last edited: Oct 7, 2005
3. Oct 7, 2005

### Astronuc

Staff Emeritus
This is not correct. The decay is essentially instantaneous.

One must think of the relativistic effects on time and distance - time dilation and length contraction.

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html

4. Oct 7, 2005

### Staff: Mentor

Don't worry about its speed after decaying. According to lab frame observers, what's the lifetime of the particle? (Hint: Time dilation.)

5. Oct 7, 2005

### Physics Monkey

Well we jumped all over this one. Haha.

6. Oct 7, 2005

### Staff: Mentor

At least we're all saying the same thing. That's good.

7. Oct 7, 2005

### asdf1

opps! lol...

8. Aug 30, 2009

### jinksys

I thought I'd piggy back on this post since I have essentially the same question.

A particle has a lifetime of 1.0E-7s when measured at rest. What distance does it travel if it is created at 0.99c?

I use the time dilation equation to find t'. I get 1.41E-8s. I then multiply this by 0.99c and get 4.19m. The book says 210m.

edit:
Got it

My book's wording gets the best of me, when it says 'at rest' it means the observer, not the particle itself.

Last edited: Aug 30, 2009