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Recent work has uncovered a consistent set of student difficulties with graphs of position, velocity, and acceleration versus time. These include misinterpreting graphs as pictures, slope/height confusion, problems finding the slopes of lines not passing through the origin, and the inability to interpret the meaning of the area under various graph curves. For this particular study, data from 895 students at the high school and college level was collected and analyzed. The test used to collect the data is included at the end of the article and should prove useful for other researchers studying kinematics learning as well as instructors teaching the material. The process of developing and analyzing the test is fully documented and is suggested as a model for similar assessment projects.
Robert J. Beichner (Mon,) studied this question.