The problem of consensus reaching with prescribed transient behavior for a group of double-integrator agents is addressed. The information exchange of the multi-agent system is described by a static communication network. We initially set timedependent constraints on the transient response of the relative positions between neighboring agents and we propose a distributed control law consisting of a proportional term of the transformed error and an additional damping term based on absolute velocities measurements. We also design an agreement protocol that can additionally achieve prescribed performance for a combined error of positions and velocities. Under a sufficient condition for the damping gains, the proposed nonlinear time-dependent distributed controllers guarantee that the predefined constraints are not violated and that consensus is achieved with a convergence rate independent of the underlying communication graph. Furthermore, connectivity maintenance can be ensured by appropriately designing the performance bounds. Theoretical results are supported by simulations.