Question

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

Answer 1

As $\Delta\tau=\Delta t\sdot\sqrt{1-v^2/c^2}$ where $\Delta t=0.100s, v=0.650c$ then $\Delta\tau\approx0.076s$