Distance vs. Time DemonstrationJessie Miller<br />Section I: Contextual Information<br />Title. Investigating Motion through Distance vs. Time Graphs<br />Grade level/content area. 12th grade physics<br />Established goals. The demonstration addresses the following standards from the Ohio Academic Content Standards and the National Science Education Standards:<br />Ohio Academic Content Standards. <br />Benchmark D, Physical Sciences. Apply principles of forces and motion to mathematically analyze, describe, and predict the net effects on objects or systems (ODE, 2004). <br />Standard 5 (grade twelve). Use and apply the laws of motion to analyze, describe, and predict the effects of forces on the motion of objects mathematically (ODE, 2004).<br />Benchmark A, Scientific Inquiry. Make appropriate choices when designing and participating in scientific investigations by using cognitive and manipulative skills when collecting data and formulating conclusions from the data (ODE, 2004).<br />Standard 2 (grade twelve). Derive simple mathematical relationships that have predictive power from experimental data (e.g., derive an equation from a graph and vice versa, determine whether a linear or exponential relationship exists among the data in a table) (ODE, 2004).<br />Standard 5 (grade twelve). Use appropriate summary statistics to analyze and describe data (ODE, 2004).<br />National Science Education Standards.<br />Science as inquiry standard levels 9-12. Abilities necessary to do scientific inquiry. Understanding about scientific inquiry (NRC, 2011).<br />Physical science standard levels 9-12. Motions and forces (NRC, 2011).<br />Section II: Big Ideas, Questioning, and Learning Outcomes<br />Understandings. This demonstration focuses on key concepts related to velocity and acceleration. Students will learn to graphically represent data and use the graphs to interpret trends in the data. Students will recognize the connection between the graphical representation of the data and the physical motion of the object being studied.<br />Essential questions. How can the slope of a distance vs. time graph be used to determine velocity? How would the distance vs. time graph for a ball moving on a flat track differ from that of a ball moving on an angled track? <br />Instructional objectives. Given a data table, students will be able to sketch and explain distance vs. time graphs with 100% accuracy. Given a distance vs. time graph, describe the motion of the object including the object’s velocity and acceleration with 100% accuracy. <br />Academic language. Distance, velocity, acceleration, force.<br />Section III: The Lesson<br />Materials. This demonstration requires: two 8 foot aluminum tracks at $40 each for a total of $80, one 1 inch steel ball bearing at $2.55 (Flinn Scientific, Inc., 2010), one wooden ramp (scrap material at no cost), and one set of 12 stop watches at $84.95 (Flinn Scientific, Inc., 2010).<br />Introduction. In this demonstration, we will be timing a steel ball’s motion on a flat track and again on an angled track. The demonstration serves to introduce students to distance vs. time graphs. Students will time the ball’s progress along each track. A distance vs. time graph will be constructed with data collected by the students for each track. The relationship between the slope of the graph and the velocity of the ball will be discussed. The flat track will show an object moving at constant velocity, so the graph will have a constant, linear slope. Students will then predict what the distance vs. time graph will look like for the angled track. The angled track will demonstrate an object which is accelerating. Students will again time the ball and create a distance vs. time graph. The slope in this case will not be constant. Students will be asked to discuss what this means in terms of velocity (velocity is changing- acceleration).<br />Hook. The “hook” for this demonstration would be along the lines of the following: “In class, we have been discussing the relationship between position, velocity, and acceleration. Today, we are going to run an actual experiment and collect our own data. We can then analyze this data by creating distance vs. time graphs and discussing what we can learn about the object’s motion from these graphs. I will have students volunteer to time the ball (two sets of four volunteers for each track, resulting in sixteen total volunteers- could be extended to three sets of four for greater participation). You (the students) will be completely responsible for data collection.” The fact that the students are collecting the data themselves should make them more engaged in the demonstration. The students will also be creating their own distance vs. time graphs.<br />Sequential outline. The demonstration will start with a description of all equipment being used: two aluminum tracks, a one-inch steel ball, a wooden ramp to initiate the ball’s motion on the flat track, and timers. There are no specific safety concerns associated with this demonstration, but students will be told not to let the steel ball fall on the floor. It may become a trip hazard, or, if dropped from a significant height, it could injure someone’s foot. Students will then be informed of the demonstration procedures. Four students will each take a timer and time the ball for a set duration of its motion on the flat track. All four will start when the ball crosses the zero point. The first student will stop when the ball reaches the 0.5-meter mark, the second will stop at the 1.0-meter mark, the third will stop at the 1.5-meter mark, and the fourth will stop at the 2.0-meter mark. The times will be recorded, and the all students will each create a distance vs. time graph for the flat track. Students will be asked to describe the graph and discuss what can be learned about the ball’s velocity from the slope of the graph. This discussion will address the essential question of how a distance vs. time graph can be used to determine velocity. Students will then predict what the distance vs. time graph will look like for the ball on the angled track. After making predictions, the same procedure that was followed for the flat track will be repeated for the angled track. The students will create a distance vs. time graph for the ball on the angled track and compare it to their predictions. The students will then discuss what this graph tells us about the ball’s velocity. The students will then compare the distance vs. time graphs for the two tracks, answering the second essential question listed. <br />Section IV: Assessment and Closure<br />Closure. The demonstration will conclude by reviewing how the slope of a distance vs. time graph for a given object relates to that object’s velocity. The difference in the distance vs. time graphs for an object moving at constant velocity and an object that is not moving at constant velocity will be used as an example for how the slope of the graph reflects the velocity of the object. The discussion of these topics should be student-lead with minimal prompting from the teacher.<br />Evidence of learning. Students will submit their distance vs. time graphs that were generated during the demonstration. Students will also be asked to include a written description of the graph and how it relates to the ball’s motion. For homework, students will complete the attached worksheet which asks them to apply ideas introduced in the demonstration to other scenarios.<br />Section V: Reference Materials<br />Flinn Scientific, Inc., (2010). Flinn chemical and biological catalog reference manual 2010. Batavia, IL: Flinn Scientific, Inc.<br />National Research Council (NRC). (1996). National science education standards. Washington, DC: National Academies Press.<br />Ohio Department of Education (ODE). (2004). Academic content standards: K-12 science. Columbus, OH: Ohio Department of Education.<br />Demonstration adapted from lab activity used in ‘Physics by Inquiry’, instructor Dr. Bruce Patton, at The Ohio State University.<br />Name____________________________<br />Distance vs. Time Graphs Review<br /><ul><li>Sketch a distance vs. time for an object which is moving at constant velocity of 1 meter/second for 3 meters then stops. Make sure your graph shows what is happening for at least five seconds.
Describe the motion of the object that is represented by the following distance vs. time graph.