The operators −i∇, the translation generators, are related to mass and velocity by a simple argument that determines the form of the Hamiltonian, in terms of the translation generators, along with the Galilei generators, for a nonrelativistic particle. For a relativistic particle, a similar discussion is given for the analogous problem of determining the position operators for an irreducible unitary representation of the Poincaré group, at least well enough to identify the velocity operators and thus identify the momentum.