This thesis aims to study the behavior of a one-dimensional granular system, composed of a cluster and a gas formed by only one grain. We analyze the behavior of long-term variables of the cluster, such as a pressure, the RMS velocity and mean space between grains, for a variety of velocity dependent coefficients of restitution. We proposed a form for the dependence of the coefficient of restitution on the relative velocity between grains, which shows as particular cases important classes of models found in the literature, such as the visco-elastic and the coefficient of restitution independent of the velocity. The results obtained show the dissolution of the cluster when there is dependence between the coefficient and speed, and permanence of the cluster when the dependence exists, in accordance with the hydrodynamic studies pointing to the transient nature of the instabilities in the density of the granular gas, whose cofficient of restitution depends on the speed.