Question

A particle has a lifetime of 0.100 s when observed while it moves at a speed of service 0.650c with respect to the laboratory. What is its lifetime in its rest frame?

Answer 1

The lifetime in its rest frame is

$$\tau=t\sqrt{1-(v/c)^2}=0.1\sqrt{1-0.65^2}=0.076\text{ s}.$$