Description of the Motion of Objects with Sub- and Superluminal Speeds

In this paper a direct derivation of the dynamics of objects moving with relativistic speeds is presented, based on two assumptions: (i) energy and mass of an object in motion are equivalent (mass-energy equivalence, known in special relativity and confirmed in experiments), (ii) an object can be considered as a variable-mass object with mass increasing with velocity (in some interpretations referred to as relativistic mass). In the presented approach the postulate on the constancy of the speed of light is not necessary. Also, the four-dimensional Minkowski spacetime is not used and no assumptions on symmetries are made. Therefore, it applies for sub- and superluminal speeds with the speed of light in a vacuum c being the critical speed, which separates the two interesting regions of speeds. The solution for v<c is fully equivalent to the results of special relativity (including the energy-momentum invariant), but the new possible solution for v>c opens an unknown and unintuitive behavior, which should be subjected to experimental investigation. In the range of superluminal speeds, a solution in which the energy of the material particle decreases as its speed increases is obtained. The critical speed in media other than a vacuum should be replaced to a speed environment-dependent, other than c.