Database applications for moving objects pose new challenges in modeling, querying, and maintenance of objects whose locations are rapidly changing over time. Previous work on modeling and querying spatio-temporal databases and constraint databases focus primarily on snapshots of changing databases. In this paper we study query evaluation techniques for moving object databases where moving objects are being updated frequently. We consider a constraint database approach to moving objects and queries. We classify moving object queries into: "past", "continuing", and "future" queries. We argue that while traditional constraint query evaluation techniques are suitable for past queries, new techniques are needed for continuing and future queries. Motivated by nearest-neighbor queries, we define a query language based on a single "generalized distance" function f mapping from objects to continuous functions from time to R. Queries in this language may be past, continuing, or future. We show that if f maps to polynomials, queries can be evaluated efficiently using the plane sweeping technique from computational geometry. Consequently, many known distance based queries can be evaluated efficiently.