A student remembers his teacher showing him how to calculate the area under the curve when the graph forms a triangle. He encounters another graph that forms a triangle shape and calculates its area, even though this problem actually requires him to find the slope. Compare graphs of position, velocity, and acceleration versus time for a given situation. Students believe kinematics variables behave identically or very similarly and should therefore be graphed identically or very similarly. A student reasons that if the acceleration is decreasing then the velocity must be decreasing.
Students see graphs as representing the physical path of motion.
Given the situation of a ball rolling down a hill, a student would draw a graph that looks like a hill. Students do not look for consistency of slopes and heights between graphs. Provide examples that require students to make qualitative comparisons between graphs. Students are unable to qualitatively discriminate between slopes. A student cannot tell which of two slopes is steeper.