In this paper, we describe the in-network processing of queries and answers, communication and mobility. We develop the analytical models to compute the system delay and the system energy consumption for P2P query processing schemes in sparse mobile networks. The analysis is based on Ordinary differential equations (ODE's) that describe the delay and energy consumption as a function of environmental parameters such as mobility, network density, and query selectivity. The analytical models enable users to choose the optimal paramers for a given environmental configuration. We validate our models in both walking and vehicular environment by simulations. The results of the simulations show good agreement with the predictions of the analytical models.