The first contribution of this paper is to compute the dynamics of the mass and of the position of the center of mass of Voronoi cells for a given multi-agent spatial distribution. These two results are then used in the design of a distributed backstepping control law for a multi-agent coverage problem. The agents are assumed to have second order dynamics and will be moving on a plane inside 3D space. The analytic expressions for the rate of change of the mass and center of mass of the Voronoi cells, valid for non-uniform density functions, are new to the best of the authors' knowledge. For the particular case of uniform density, the result of the rate of change of area was known before but a new proof is presented in the paper based on a geometric argument and small perturbations. Simulation results are provided to show the effectiveness of the approach.