This paper describes a systematic investigation of the understanding of the concept of velocity among students enrolled in a wide variety of introductory physics courses at the University of Washington. The criterion selected for assessing understanding of a kinematical concept is the ability to apply it successfully in interpreting simple motions of real objects. The primary data source has been the individual demonstration interview in which students are asked specific questions about simple motions they observe. Results are reported for the success of different student populations in comparing velocities for two simultaneous motions. It appears that virtually every failure to make a proper comparison can be attributed to use of a position criterion to determine relative velocity. Some implications for instruction are briefly discussed.