SOLUTIONS Workshop 2: Reading Graphs, Motion in 1-D

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1 SOLUTIONS Workshop 2: Reading Graphs, Motion in 1-D Question 2. Dueling Position Graphs This set of questions gets at a common confusion the difference between position and velocity on position graphs. (a) Which object s speed is larger at t = 13 sec? What makes you think so?: Speed is the absolute value of velocity, and velocity is the slope of position. Object 2 has a greater slope at t=13. (b) Which object s position is greater at t = 13 sec? What makes you think so?: Object 1 has a greater position. (c) Sometimes, answering part B causes a student to go back and change their answer to part A. Why do you think this is? What reasoning error that a student might make in part A is likely to be caught when the student then does part B?: This error occurs when one confuses position with velocity when reading these graphs. (d) At approximately what time do the objects have the same velocity? How do you tell from the graph?: They have the same velocity when the slope is equal. This happens around 11s. (e) How far apart are the objects when they have the same velocity? Explain how you know: The difference in position at this point is roughly 80 meters. Often people will 3s and 15s for part d, because they ve confused position with velocity. (f) Sketch a rough graph of Object 2 s velocity vs. time from t = 0 to t = 12, and explain your reasoning. 1

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7 Describing motion with graphs The purpose of these problems is to get an intuitive feel for interpreting graphs. The important thing is to be able to qualitatively describe what is happening in the graph. Therefore, the explanations in these solutions should not be treated as a set of rules to memorize/follow. It is more important to make sure that students are reasoning about the graphs. (a) At which of the lettered points on the graph below: is the motion slowest?: Velocity is the slope of the line, so motion is the slowest when the slope of position is closest to zero. We see that the position graph is mostly flat at points B and F. is the person speeding up?: Acceleration is the derivative of velocity, and can be determined by the concavity of the graph (concave up=positive acceleration; concave down = negative acceleration). When we use the phrase speeding up colloquially, we typically mean when speed is increasing, meaning when velocity is in the same direction as acceleration. Point D roughly looks like the velocity and the accerlation are both negative. is the person slowing down?: The phrase slowing down colloquially refers to when speed is decreasing, or when acceleration and velocity are in opposite directions. This looks like it happens at Point A. is the person reversing direction?: This is one that students can easily get stumped on. Reversing direction refers to when the velocity changes sign. At point B, the velocity changes from positive to negative. (b) A common mistake is to say the person reverses direction at point E. Why do you think a student might make that mistake? What might you say to them to help them avoid that mistake in the future? At point E, the position switches from positive to negative. However, the direction of motion is the same. Students often confuse position and velocity. 7