$(5$ pt $)$ A $+$ particle has a mean lifetime of $80\mathrm{.}2$ ps $.$ A physicist measures that mean lifetime to be $403$ ps as a particle moves in his lab. The rest mass of the particle is $2\mathrm{.}12{10}^{-27}kg.($a$)$ How fast is the particle moving? $($b$)$ How far does it travel, as measured in the lab frame, over one mean lifetime? $($c$)$ What are its rest, kinetic, and total energies in the lab frame of reference? $($d$)$ What are its rest, kinetic, and total energies in the particle's frame?