Question

A certain particle at rest has a lifetime of 2.52 mu s. what must be the speed of the particle for its lifetime observed to be 8.32 mu s? 0.985c 0.953c 0.913c 0.302c None of the above

Answer 1

Answer:

0.953c

Explanation:

T₀ = lifetime of the particle at rest = 2.52 μs

T = Observed lifetime of the particle while in motion = 8.32 μs

v = speed of particle

c = speed of light

Using the formula for time dilation

$T = \frac{T_{o}}{\sqrt{1-(\frac{v}{c})^{2}}}$

inserting the values

$8.32 = \frac{2.52}{\sqrt{1-(\frac{v}{c})^{2}}}$

v = 0.953c