Answer
See answers.
Work Step by Step
Find the speed of the particle in the lab frame.
$$v=\frac{1.00m}{3.40\times10^{-9}s}=2.941\times10^8 m/s=0.9811c$$
a. Find the lifetime in the rest frame by using equation 26–1a.
$$\Delta t_0=\Delta t_{lab}\sqrt{1-v^2/c^2}=(3.40\times10^{-9}s) \sqrt{1-0.9811^2}=6.6\times10^{-10}s$$
b. In the rest frame, the particle traveled a distance equal to its speed multiplied by the rest lifetime.
$$\Delta x_0=v\Delta t_0=(2.9412\times10^8 m/s)(6.584\times10^{-10}s)=0.19m$$