In the relativistic uniform model for continuous medium, the integral theorem of generalized virial is derived, in which generalized momenta are used as particles’ momenta. This allows us to find exact formulas for the radial component of the velocity of typical particles of the system and for their root-mean-square speed, without using the notion of temperature. The relation between the theorem and the cosmological constant, characterizing the physical system under consideration, is shown. The difference is explained between the kinetic energy and the energy of motion, the value of which is equal to half the sum of the Lagrangian and the Hamiltonian. This difference is due to the fact that the proper fields of each particle have mass–energy, which makes an additional contribution into the kinetic energy. As a result, the total energy of motion of particles and fields is obtained.