Motion and Displacement: Understanding the Vocabulary

1. Motion • Vocabulary: • motion • displacement (Δx) • vector • magnitude • sign convention • distance (d) • scalar • average velocity (v) • rate • instantaneous velocity (v) • speed (s) From “Here” to “There” “Nude Descending a Staircase, No. 2” (1912) Marcel Duchamp This topic can be found in your textbook on pp. 40-47.

2. What is meant by “motion”? • A change in position within a particular frame of reference.

3. Displacement (Δx) • The length of the straight line* drawn from an object’s initial position to the object’s final position. It is a vector** quantity. Δx = xf – xi *the path that the object took to get from xi to xf is not relevant! **a vector has both magnitude and direction

4. Displacement Sign Conventions +y • Right: +x or east • Left: -x or west • Up: +y or north • Down: -y or south • Out of page: +z • Into page: -z -z -x +x +z -y

5. Try these: • Watch the animation carefully. What is the displacement of the blue dot? • Δx = xf – xi = -5cm – 1cm = -6cm Units are centimeter

6. Try these: • Watch the animation carefully. What is the displacement of the red dot? • Δx = xf – xi = 4cm – (-7cm) = 11cm Units are centimeter

7. Try these: • Watch the animation carefully. What is the displacement of the purple dot? • Δx = xf – xi =-2cm – 8cm = -10cm Units are centimeter

8. Distance (d) • Distance is not the same as displacement. Displacement does not depend upon the path taken to get from the initial position to the final position whereas distance does. • Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. The direction does not matter.

9. Practice: If Bob Loblaw walks the following path, what is Bob’s a) distance travelled, and b) displacement? Answers: d = 2.0 km Δx = 2.0 km north 2.0 km

10. Practice: If Bob Loblaw walks the following path, what is Bob’s a) distance travelled, and b) displacement? 2.0 km Answers: d = 4.0 km Δx = 2.8 km northeast 2.0 km

11. Practice: If Bob Loblaw walks the following path, what is Bob’s a) distance travelled, and b) displacement? 2.0 km Answers: d = 6.0 km Δx = 2.0 km east 2.0 km 2.0 km

12. Practice: If Bob Loblaw walks the following path, what is Bob’s a) distance travelled, and b) displacement? 2.0 km Answers: d = 8.0 km Δx = 0.0 km 2.0 km 2.0 km 2.0 km

13. Question • What is your displacement from when you get out of bed, eat breakfast, go to school, eat lunch, hang out with friends, do your homework, eat dinner, and go to bed? • Answer: 0 m

14. Practice What is the distance and the displacement of Hamlet the Hamster who travels from point A to point B to point C and ends up at point D? 40 m 100 m 40 m C A D B

15. Practice What is the distance and the displacement of Hamlet the Hamster who travels from point A to point B to point C and ends up at point D? 40 m 100 m 40 m C A D B

16. Practice What is the distance and the displacement of Hamlet the Hamster who travels from point A to point B to point C and ends up at point D? 40 m 100 m 40 m C A D B Answer: d = 420 m and Δx = 140 m to the right

17. Average Velocity (v) • Velocity refers to the rate* at which an object changes its position. It is a vector quantity (must include a direction!) SI Unit: m/s *rate always refers to a change in something over time.

18. Practice • A chicken travels 36 km to the north in 30.0 min. Find its average velocity in km/min and in km/h. Answers: • 1.2 km/min north • 72 km/hr north

19. Practice • Iona Ford drives her car with an average velocity of 24 m/s toward the east. How long will it take her (in hours) to drive 560 km on a perfectly straight highway? Answer 6.5 hr

20. Instantaneous velocity • Velocity at one moment in time.

21. Question • In what situations might you be more interested in instantaneous velocity and in what situations might you be more interested in average velocity?

22. Average Speed (s) • Average speed is not the same as average velocity. Speed has no direction. SI unit: m/s

23. Practice • Inna Hurrie runs 7.5 km north from her house and then turns around and runs 5.0 km south to her friend’s house. The entire trip takes 1.25 hours. a) what was her distance travelled?; b) what was her displacement?; c) what was her average speed?; and d) what was her average velocity? • Answers • a) 12.5 km • b) 2.5 km north • c) 10.0 km/hr • d) 2.0 km/hr north

24. Practice • In which of the following do speed and velocity have the same magnitudes? • Running a 400 m race in 50 s on a race track. • Driving through Nebraska for one hour with the cruise control set at 55 mph. • Driving to Chipotle for lunch, eating, then heading back to school for 6th period. • Going from 0 to 60 mph in 3.4 seconds on a drag racing track.

25. More practice • What is wrong with the following statement? “The car traveled around the track at constant velocity.” • The average velocity for a trip has a positive value. Is it possible for the instantaneous velocity at any point to have a negative value?  • If average velocity is non-zero for some time interval, does this mean that the instantaneous velocity is never zero during this interval? Explain.  4. What are the three mechanisms in your car to change your velocity?

26. Even more practice • A car travels 100.0 km to the east. If the first half of the distance is driven at 50.0 km/h and the second half at a 100.0 km/h, what is the average velocity? • Answer • 66.7 km/h to the east (Why isn’t the answer 75 km/h which is the average of 50.0 km/h and 100.0 km/h?)

27. Motion Summary Equation Summary • Δ = f – i