Engage 1. Compare the total distance traveled between A and B, if both paths arrive at the factory.

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1 Unit 1: Phenomenon The Physics of Skydiving Lesson 2.f Displacement and Velocity Student Performance Objectives Students will define displacement. Students will define velocity. Students will differentiate between total distance traveled and displacement. Students will determine the velocity of objects moving with a uniform linear velocity given displacement and time. Students will solve one dimensional velocity problems. DO NOT WRITE ON THIS HANDOUT Engage 1. Compare the total distance traveled between A and B, if both paths arrive at the factory. 2. If the motorcyclist was able to travel to the factory along either path and arrive at the factory in 2 hours, along which path would it have to have a greater average speed? 3. A person walks 5.00 meters away from his starting position, turns around and walks 2.75 meters in the opposite direction. What is the total distance the person has walked? 4. How far away is the person from his original starting position? 5. If average speed is a comparison of the total distance traveled to time, what is the average speed of the person if the entire trip took 3.10 seconds? Show your work 6. Suppose we only consider the distance between the starting position and the ending position. How fast did the person travel given this shorter distance? Show your work Notes and Definitions A. Position A specific location in an established frame of reference. Variable: initial position x 0 Final position x B. Change in Position or Displacement The distance traveled between the initial position and the final position, while moving in a constant direction Variable: x (the Greek letter delta is used to indicate the change of in the variable. You find by subtracting the final value minus the initial value; in our case the final position minus the initial position) Units are meters m Displacement is a vector quantity: it has magnitude (size) and direction (ex. North-east) The direction can be represented (+) or (-) signs, compass directions (N, S, E, W), or angle measures relative to a given axis C. Distance The path length traveled along a continuous path from the origin to the endpoint. Multiple direction changes are possible. Variable = x or d Units are meters m Distance is a scalar quantity: it only has magnitude (size) D. Scalar quantities have a magnitude only (a numerical value ex. 5.0 m), and no direction. Ex. Mass, temperature, speed, and distance 1

2 E. Vector quantities have a magnitude and a direction. Ex. Displacement 5 m west, (-) 5 m, 5 m at 32 north of west or Velocity - 5m/s, 5m/s away from the motion detector F. Average Speed and Total Distance Average Speed = Total Distance/Time (Average Speed - x/ t) v = x/ t Variable = v. The bar indicates that the quantity is an average. Units are meters per second ( m/s ) Average speed is a scalar quantity. G. Velocity The speed of an object in a specific direction. Variable = v Units = m/s in a particular direction. Velocity = displacement/time v= x/ t Velocity is a vector quantity. Explore In your own words and your own examples and Practice Problems 7. What is position? 8. What is a change in position? 9. What is average speed? 10. What is total distance? 11. Are direction changes possible when measuring total distance? 12. What variables are used to represent total distance? 13. What units are used to measure total distance? 14. What kind of quantity is total distance? 15. What is a scalar quantity? 16. What is magnitude? 17. Give an example of a scalar measurement. 18. What equation is used to determine average speed given total distance and time? 19. What variable is used to represent average speed? 20. What units are used to represent total speed? 21. What kind of quantity is average speed? 22. What is displacement? 23. How can the direction of displacement be represented? 24. What variable is used to represent displacement? 25. What units are used to measure displacement? 26. What kind of quantity is displacement? 27. What do vectors have? 28. Give examples of vector quantities. 29. What is velocity? 2

3 30. What variable is used to represent velocity? 31. What units are used to measure velocity? 32. What equation is used to determine velocity? 33. What kind of quantity is velocity? 34. What do vector quantities have? 35. Give examples of velocity vector quantities. 36. Sample problem. A toy train travels 1.25 m to the right in 2.50 s. The train then reverses course and backs up 0.50 m in 1.00 s. b. What is the average speed of the train? show work c. What is the displacement of the train relative to its starting position? show work d. What is the velocity of the train? show work 37. A bee travels 12.0 m north in 3.0 s. The bee then reverses direction, and travels 4.0 m south in 2.0 s. b. What is the average speed of the bee? show work c. What is the displacement of the bee relative to its starting position? show work 38. The graph illustrates the position of an object with respect to time. a. What is the velocity of the object from 0.0 to 3.0 seconds? show work b. Graph that velocity on the provided grid. c. What is the velocity of the object from 3.0 to 6.0 seconds? show work d. Graph the velocity on the provided grid. e. What is the final displacement of the object relative to its starting position? show work f. What is the velocity of the object over the entire time interval? show work 3

4 39. The graph below illustrates the position of an object with respect to time. a. What is the velocity of the object from 0.0 to 2.0 seconds? show work b. Graph that velocity on the provided grid. c. What is the velocity of the object from 2.0 to 6.0 seconds? show work d. Graph that velocity on the provided grid. e. What is the final displacement of the object relative to its starting position? show work f. What is the velocity of the object over the entire time interval? show work 40. The graph below illustrates the velocity of an object with respect to time. Assume the object has an initial position of 0.0 m. a. What is the change in position experienced by the object from 0.0 to 3.0 seconds? b. Graph the position of the object from 0.0 to 3.0 seconds. c. What is the change in position experienced by the object from 3.0 to 6.0 seconds? d. Graph the position of this object at 6.0s. Remember, you must begin the line at the position where the object is located at 3.0 seconds. e. What is the final displacement of the object at 6.0 seconds? f. What is the velocity of the object over the entire time interval? 41. The graph below illustrates the velocity of an object with respect to time. Assume the object has an initial position of 0.0 m. a. What is the change in position experienced by the object from 0.0 to 4.0 seconds? b. Graph the position of the object from 0.0 to 4.0 seconds. c. What is the change in position experienced by the object from 4.0 to 6.0 seconds? 4

5 d. Graph the position of this object at 6.0s. Remember, you must begin the line at the position where the object is located at 4.0 seconds. e. What is the final displacement of the object at 6.0 seconds? f. What is the velocity of the object over the entire time interval? Explain 42. Match the terms and definitions in the table below. 1. Position A. Quantities that have a magnitude only (a numerical value ex. 5.0 m), and lack a direction. 2. Position B. meters/second or m/s 3. Average Speed C. A specific location in an established frame of reference. 4. Vector D. meters/ second in a particular direction (ex. 5.0m/s west, or +2.5m/s) 5. Scalar E. The speed of an object in a specific direction. 6. Total Distance F. meters in a particular direction (ex. 5.0 m south, or -3.2 m) 7. Displacement G. The distance traveled along a continuous path from the origin to the endpoint. 8. Velocity H. meters 9. Average Speed Units 10. Velocity Units J. v Displacement Units Total Distance Units Average Speed Variable 14. Velocity Equation N. v = Δx Δt 15. Average Speed Equation I. Quantities that have a magnitude and a direction. K. The net distance from the origin to the end point, and the direction of the net distance. L. v = Δx Δt & direction M. The distance traveled between the initial position and the final position. or Δd Δt O. A change in position relative to time - or - Total Distance/ T 43. Solve the following problems. A hummingbird travels 50.0 m to the right in s. The hummingbird then reverses course and backs up 10.0 m in 4.0 s. b. What is the average speed of the hummingbird? show work c. What is the displacement of the hummingbird relative to its starting position? show work d. What is the velocity of the train? show work 5

6 44. A butterfly travels 7.8 m to the right in 3.2 s. The butterfly then reverses course and backs up 7.1 m in 2.8 s. b. What is the average speed of the butterfly? show work c. What is the displacement of the butterfly relative to its starting position? show work d. What is the velocity of the butterfly? show work 45. A radio controlled car travels 22.3 m to the right in 9.50 s. The car then reverses course and backs up 61.2 m in 20.0 s. b. What is the average speed of the car? show work c. What is the displacement of the car relative to its starting position? show work d. What is the velocity of the car? show work 6

7 Elaborate Group Problem Solving In this exercise, you will be assigned to a group, and be required to develop a solution to one of the following problems. Your group will present your solution to the class. Problem 1 Car A has an average speed of 2.0 m/s. Car B has an average speed of 3.0 m/s. The cars depart at the same time. Determine their final separation after 1.00 minute. Problem 2 Car A has an average speed of 4.0 m/s. Car B has an average speed of 1.0 m/s. The cars depart at the same time. Determine their final separation after 1.00 minute. Problem 3 Car A has an average speed of 6.0 m/s. Car B has an average speed of 3.0 m/s. The cars depart at the same time. Determine their final separation after 1.00 minute. Problem 4 Determine the average speed of the object for the following intervals. A-B A-D A-G Determine the final displacement of the object. Problem 5 Determine the change in position from B to C. Determine the velocity from B to C. Determine the change in position from E to F. Determine the velocity from E to F. Determine the change in position from F to G. Determine the velocity from F to G. Problem 6 Determine the average speed for the full 9.0 second interval. Determine the velocity of the object for the following intervals: seconds. 6.5 to 7.5 seconds. 7.5 to 9.0 seconds. 3.0 to 6.5 seconds. If the (+) direction is to the right and the (-) direction is to the left, is the object to the right or the left of the origin at t=7.0 s? Problem 7 Determine the average speed for the full 9.0 second interval. Determine the velocity of the object for the following intervals: seconds. 3.0 to 4.3 seconds. 4.3 to 6.5 seconds. 7.5 to 9.0 seconds. If the (+) direction is to the right and the (-) direction is to the left, is the object to the right or the left of the origin at t=5.0 s? Problem 8 How much time will pass before the runners meet? How far will the runner on the left travel in the given time? How far will the runner on the right travel in the given time? Assuming the origin is the starting point of the runner on the left, at what position will the runners meet? 7

8 Problem 9 An object moves with the velocities described on the right. Assume initial position = 0.0 m. Determine position at the following times: 1.5 sec. 3.0 sec. 4.5 sec. 6.0 sec. Assign a scale to the position vs. time graph. (hint: if you have negative position values, start 0 above the origin) Plot the position vs. time data for the object. 8