A mobile wireless delay-tolerant network (DTN) model is proposed and analyzed, in which infinitely many nodes are initially placed on R^2 according to a uniform Poisson point process (PPP) and subsequently travel, independently of each other, along trajectories comprised of line segments, changing travel direction at time instances that form a Poisson process, each time selecting a new travel direction from an arbitrary distribution; all nodes maintain constant speed. A single information packet is traveling towards a given direction using both wireless transmissions and sojourns on node buffers, according to a member of a broad class of possible routing rules. For this model, we compute the long-term averages of the speed with which the packet travels towards its destination and the rate with which the wireless transmission cost accumulates. Because of the complexity of the problem, we employ two intuitive, simplifying approximations; simulations verify that the approximation error is typically small. Our results quantify the fundamental trade-off that exists in mobile wireless DTNs between the packet speed and the packet delivery cost. The framework developed here is both general and versatile, and can be used as a starting point for further investigation.