Speed of a Relativistic Particle?

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SUMMARY

The discussion focuses on calculating the average speed of a relativistic particle, specifically Particle X, which has a lifetime of 256.2 picoseconds and leaves an average track of 21.8 cm before decaying. To determine its speed in terms of the speed of light, one must consider relativistic effects rather than using the classical equation d=vt. The relationship between the particle's lifetime and track length is crucial for applying the correct relativistic equations, such as those involving time dilation and Lorentz transformations.

PREREQUISITES
  • Understanding of relativistic physics concepts
  • Familiarity with particle decay and lifetime measurements
  • Knowledge of Lorentz transformations
  • Basic grasp of speed calculations in physics
NEXT STEPS
  • Research the principles of time dilation in special relativity
  • Learn about Lorentz transformations and their applications
  • Study the behavior of muons and their relevance to relativistic speed tests
  • Explore the equations governing particle decay and speed calculations
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Students studying physics, particularly those focusing on particle physics and special relativity, as well as educators seeking to explain relativistic effects in particle behavior.

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Homework Statement



Particle track detectors are used to measure the speed of particles if the lifetime of the particle is known. Particle X has a lifetime of 256.2 ps. These particles are created in an experiment inside the detector by a given reaction. The particles leave 21.8 cm long tracks on average before they decay into other particles not observable by the detector.
What is the average speed of the particles in terms of the speed of light?


Homework Equations



Not sure?



The Attempt at a Solution


While this is a question of relativistic speed of the particle... I'm not sure what the average track length relates to the lifetime of the particle? Can anyone point me in the direction of the relevant equations? Thanks
 
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The particles come into existence inside the detector. They travel some distance in some time, then decay and disappear. If this were non-relativistic, you could just do d=vt, sub in the lifetime as t and the track length as d. But it's relativistic - what do you do?

PS: You might want to look up muons in relation to tests of special relativity.
 

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