Table 1 Motion Total Distance Covered Motion A Motion B

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1 And thus, since God is the First Mover, simply, it is by His motion that everything seeks to be likened to God in its own way. Summa Theologica, IIa:Q109,A6 Time (sec) Table 1 Motion Total Distance Covered Motion A Motion B savg 1 ft/sec: 10 ft 10 sec 2.5 ft/sec: 10 ft 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 1

2 Table 2 Comparison of Velocities Motion A Motion B Time Interval Distance traveled Avg. Vel Distance traveled Avg. Vel 0-1 sec 1 ft 1 ft/sec 1 ft 1 ft/sec 1-2 sec 1 ft 1 ft/sec 2 ft 2 ft/sec 2-3 sec 1 ft 1 ft/sec 3 ft 3 ft/sec 3-1 ft 1 ft/sec 4 ft 4 ft/sec 4-5 sec 1 ft 1 ft/sec sec 1 ft 1 ft/sec sec 1 ft 1 ft/sec sec 1 ft 1 ft/sec sec 1 ft 1 ft/sec sec 1 ft 1 ft/sec v avg = d t = d f d 0 t f t 0 Time Interval Table 3 Comparison of Acceleration Motion A Motion B Difference in Velocities Acceleration (ft/sec 2 ) Difference in Velocities Acceleration (ft/sec 2 ) 0 10 sec. 0 ft/sec 0 ft/sec 2 3 ft/sec 3 ft/sec 2 a = v t 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 2

3 Data Analysis and Conclusions 1. Average Speed a. Compare your average speed in Motion A with that in Motion B In Motion A, the average speed was 1ft/sec. In Motion B, the average speed was 2.5ft/sec. b. Describe this new speed in the second experiment. Were you simply walking faster at a uniform pace? Explain. In the second experiment the student was NOT simply going 2.5-times as fast. This speed represents an average speed. In fact, the speed was increasing with each 1- second increment. c. Does a value for average speed give any information on the direction of motion? No, speed gives no reference to direction of motion. d. Does a value for average speed give any information on the type of motion that is whether the motion is uniform or accelerating? No, as we see above, the value is simply an average over a time period. During that time period, the object may have experienced uniform motion, or increasing or decreasing motion. 2. Distance vs. Time Graph: a. Compare and contrast your curve for Motion A with that of Motion B in a few brief sentences. Accept reasonable answers that demonstrate the student is critically evaluating the Distance vs. Time graph. b. Is it clear from the curve whether the person in Motion B is simply going about twice or fast, or whether the person is accelerating? Answers will vary. Some students may draw a straight line through the points and will not observe acceleration. Other students may draw a curve or point-to-point between data and will detect acceleration. 3. Comparison of Velocities: a. Review data in Table 2 as well as the Velocity vs. Time graph. Compare the trend in velocities between Motion A and Motion B. Accept reasonable answers that demonstrate the student is critically evaluating the Velocity vs. Time graph. b. Is Motion A uniform motion or acceleration? Explain. Motion A is uniform motion since the average velocity does not change between 1- second intervals. c. Is Motion B uniform motion or acceleration? Explain. Motion B demonstrates acceleration since the average velocity DOES change between 1-second intervals Catholic Initiatives in Math and Science, LLC All Rights Reserved 3

4 4. Acceleration: a. Compare the acceleration calculated for Motion A with that for Motion B. Motion A has no acceleration (a=0 ft/sec/sec). Motion B does exhibit acceleration of 3 ft/sec/sec. b. Which graph best demonstrates acceleration? The Velocity vs Time graph best demonstrates acceleration. c. You calculated acceleration from Data Table 2: Comparison of Velocities. Explain how you could also calculate acceleration from a graph? Which graph would you use to calculate acceleration? The Velocity vs Time graph should be used. In this graph, the slope (slope = rise/run) of the line yields the acceleration (Δv/Δt). To obtain the slope the student has two options. A liner regression of the line would yield the slope. Or, the student could find the rise/run between last value and first value of the line. d. In Motion B you calculated a certain acceleration. For every second that elapsed, by how much did your velocity change? For every second that elapses, the student is increasing velocity by 3 ft/sec. This is the meaning of an acceleration of 3 ft/sec/sec (3 ft/sec 2 ). 5. A student performed a similar experiment. His data and Distance vs. Time graph is below. STUDENT IS MOVING IN THE + DIRECTION. a. Calculate the velocities between 0-1, 1-2, 2-3 and 3-onds. Then construct a Velocity vs Time graph. Make sure to label all parts of the graph Include units with every number A data table and a graph are provided for your use Time Increment Δd Velocity (per 1 sec increment) (change in distance) 1 sec 4 ft 4 ft/sec 2 sec 3 ft 3 ft/sec 3 sec 2 ft 2 ft/sec 1 ft 1 ft/sec 2015 Catholic Initiatives in Math and Science, LLC All Rights Reserved 4

5 b. What type of motion is this? The student is slowing down - This motion is acceleration. c. Did the student accelerate? If so, which type of acceleration? Yes, this was Negative Acceleration. It is acceleration because the velocity is changing. It is Negative Acceleration because the student is slowing down in the + direction. Some call this motion deceleration, however this is not a proper physics term for this motion. d. In the experiment, you calculated an acceleration value for Motions A and B. Using the data you placed in the table above (question 5a), calculate acceleration between Second 1 and Second 4. Show your calculations and make sure your answer has both a numerical value and units. a = [1 ft sec 4 ft sec ] = 3 sec = ft/sec Catholic Initiatives in Math and Science, LLC All Rights Reserved 5