A newly discovered subatomic particle, the S meson, has a mass M. When at rest, it lives for exactly τ = 3×10⁻⁸ seconds before decaying into two identical particles called P mesons (peons?) that each have a mass of αM.
a. In a reference frame where the S meson is at rest, determine
i. the kinetic energy,
ii. the momentum, and
iii. the velocity
of each P meson particle in terms of M, α, the speed of light c, and any numerical constants.
b. In a reference frame where the S meson travels 9 meters between creation and decay, determine
i. the velocity and
ii. kinetic energy of the S meson.
Write the answers in terms of M, the speed of light c, and any numerical constants.