Question

A certain type of elementary particle travels at a speed of 2.50x108 m/s. At this speed, the average lifetime is measured to be 2.76x10-6 s. Part A What is the particle's lifetime at rest? Express your answer with the appropriate units. ? M: HÅR Value O 2 Units Ato = Submit Request Answer Provide Feedback

Answer 1

Using time dilation formula,

t'=t $\sqrt{}$ (1-(v^{​​​​​​2}​​​/c^{​​​​​​2} ))

Given,

t'=2.76x10^-6 s

v=2.50x10⁸ m/s

c=3x10⁸ m/s

Therefore putting values,

t' = t√(1-(2.5 x 10⁸/ 3 x 10⁸)²)

=> t' = 0.552t

=> t= t'/0.552 = 2.76x10^-6s/0.552

=> t = 5x10^-6 s