Two important questions concerning cosmic rays are: Why are electrons in the cosmic rays less efficiently accelerated than nuclei? How are particles accelerated to great energies in ultra-high energy cosmic rays? In order to answer these questions we construct a simple model of the acceleration of a charged particle in the cosmic ray. It is not meant as a detailed model, which is expected to be rather complicated, but rather as a "pedagogic model" pointing out some important elements of a more complete model. Furthermore, the present model is sufficiently simple that it may be suitable as an "astrophysical example" in the teaching of the special theory of relativity. In this model a particle is accelerated by ultrarelativistic shocks in a source of gamma ray bursts. No assumption as to the details of the accelerating mechanism is made except that the force acting on a charged particle depends only upon the charge of the particle and not upon its mass, and the product of the force and the thickness of the shock waves must be sufficiently great. It is important for the success of the model that the energy radiated by the particles is taken mainly from the Schott energy and not from the kinetic energy of the particles. It is shown how this model of the accelerating process can explain why electrons are accelerated to less energy than protons and heavier nuclei. The mechanism also explains how particles may be accelerated to energies greater than 10[superscript 20] eV.