In this paper we study the evolutionary dynamics of the public goods game in a population of mobile agents embedded in a two-dimensional space. In this framework, the backbone of interactions between agents changes in time, allowing us to study the impact that mobility has on the emergence of cooperation in structured populations. Our results point out that a low degree of mobility enhances cooperation in the system. In addition, we study the impact of the size of the groups in which games are played on cooperation. Again we find a rise and fall of cooperation related to the percolation point of the instant interaction networks created by the set of mobile agents.