This paper addresses the problem of reachability for timed models handling additional quantities progressing linearly such as distance of moving objects to a target. We first introduce a variant of Petri nets called trajectory nets where some places are standard control places containing tokens, and other places contain a simplified representation of trajectories of objects instead of tokens. We give a semantics for this model, and propose an abstraction of sets of equivalent configurations into symbolic domains. We show how to compute in polynomial time a symbolic representation of successors of configurations appearing in a domain, and prove that domains are closed under calculus of successors. Further, the set of domains for a fixed trajectory net is finite. When the control part of the model is bounded, reachability, coverability and safety properties involving distances can be checked in PSPACE on a sound, complete, and finite abstraction called a state class graph.