The hot and dense matter produced in nucleus–nucleus collisions is supposed to expand accordingto unified hydrodynamics, one of the few theoretical models that can be worked out exactly. The solutionis then used to formulate the rapidity distribution of charged particles frozen out from the fluid on thespace-like hypersurface with a fixed temperature, $T_{FO}$. A comparison is made between the theoretical predictions and the experimental measurements carried out by PHOBOS Collaboration in the Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory (BNL) in different centrality Au–Au and Cu–Cu collisions at $\sqrt{s_{NN}}$=19.6 and 22.4 GeV, respectively. The theoretical results are in good accordance with experimental data.