Answer:
[tex]1.3922\times 10^{-8}\ s[/tex]
Explanation:
[tex]\Delta x[/tex] = Distance covered = 1 m
[tex]\Delta t_l[/tex] = Time taken = 3.44 ns
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
Velocity would be
[tex]v=\frac{\Delta x}{\Delta t_l}\\\Rightarrow v=\frac{1}{3.44\times 10^{-9}}\\\Rightarrow v=290697674.4186\ m/s[/tex]
Time in rest frame is given by
[tex]\Delta t'=\frac{\Delta t_l}{\sqrt{1-\frac{v^2}{c^2}}}\\\Rightarrow \Delta t'=\frac{3.44\times 10^{-9}}{\sqrt{1-\frac{290697674.4186^2}{(3\times 10^8)^2}}}\\\Rightarrow \Delta t'=1.3922\times 10^{-8}\ s[/tex]
It lived [tex]1.3922\times 10^{-8}\ s[/tex] before decaying
