We examine a discrete model of sticky particles initially subjected to acceleration. We propose a novel generalized variational principle for characterizing clusters (i.e., particle agglomerations) under decreasing acceleration function. This accelerated particle model is usually employed to solve a system of forced (inhomogeneous) pressureless gas equations. The momentum conservation law requires evaluating the force acting on the gas particles. Here, we present a new solution to this system of equations, based on the distribution of mass over particle velocities and on the acceleration function.