The proper choice of a measurement technique that minimizes systematic and random uncertainty is an essential part of experimental physics. These issues are difficult to teach in the introductory laboratory, though. Because most experiments involve only a single measurement technique, students are often unable to make a clear distinction between random and systematic uncertainties, or to compare the uncertainties associated with different techniques. In this paper, we describe an experiment suitable for an introductory college-level (or advanced high school) course that uses velocity measurements to clearly show students the effects of both random and systematic uncertainties. (Contains 1 figure.)