Question

a certain type of elementary particle travels with a speed of 2.70 x 10∧8 m/s. at this speed, the half-life is measured to be 4.76 x 10 ∧ -6 s. what is the lifetime of the particle at rest?

Answer 1

The lifetime of the particle at rest

$$\tau=\Delta t\sqrt{1-\frac{v^2}{c^2}}$$

$$\tau=4.76*10^{-6}\sqrt{1-\frac{(2.7*10^8)^2}{(3.0*10^8)^2}}=2.07*10^{-6}\;\rm s$$