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The expressions of momentum and energy of a particle in special relativityare often derived in a quite unconvincing manner in elementary text, byresorting either to electrodynamic or quantum considerations, or via theintroduction of the less-than-elementary concept of a four-vector. It isinstead possible, by exploiting considerations introduced by P. Epstein and A.Einstein and exploited later by Feynman, to obtain a fully elementaryderivation of these expressions and of the $E=mc^2$ formula exploiting onlyLorentz transformations and the postulate of the conservation of quantitiesdefined for point-like particles which reduce to the Newtonian expressions ofmomentum and energy in the classical limit.

Elementary derivation of the expressions of momentum and energy in special relativity