Describing Motion

1. Describing Motion Motion Displacement Speed & Velocity Acceleration Graphing Motion

2. I. Motion

3. A. Motion • Problem: • Is your desk moving? • We need a reference point... • nonmoving point from which motion is measured

4. Reference point Motion A. Motion • Motion • Change in position in relation to a reference point.

5. A. Coordinate Systems • A system used to describe motion that indicates where the zero point (reference point) of the variable being studied is located and the direction in which the values of the variable increase • Every coordinate system has an origin • Origin • The point in a coordinate system at which the variable have a zero value

6. Vector Quantity A quantity that has both magnitude and direction Ex. 30 m/s due East Scalar Quantity A quantity that has only magnitude Ex. 30 m/s B. Vectors and Scalars

7. II. Displacement

8. A. Distance vs. Displacement • Distance • Scalar • How much ground an object covers during its motion • Displacement • Vector • Object’s change in position

9. B. Displacement • The change in position of an object • Displacement is not equal to distance traveled • Displacement can be positive or negative Displacement = change in position = final position - initial position d = df -di

10. B. Displacement • A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

11. B. Displacement • Use the diagram to determine the distance traveled by the skier and the resulting displacement during these three minutes

12. B. Displacement • Use the diagram to determine the distance traveled by the skier and the resulting displacement during these three minutes • Distance – 420 m • Displacement – 140 m rightward

13. B. Displacement • What is Seymour's resulting displacement and distance of travel?

14. B. Displacement • What is Seymour's resulting displacement and distance of travel? • Distance - 95 yards • Displacement - 55 yards left

15. B. Displacement Practice Problems • 1. What is the displacement of the CDHS cross-country team if they begin at the school, run 10 miles and finish back at the school? • 2. What is the distance and the displacement of the race car drivers in the Indy 500?

16. III. Speed and Velocity

17. d v t A. Speed & Velocity • Speed • rate of motion • distance traveled per unit time

18. A. Speed & Velocity • Velocity • Speed with Direction • Average Velocity • Displacement at a given time • Total displacement divided by the time interval during which the displacement occurred Change in position Displacement Average Velocity = = Change in time Time interval ∆ d df - di v = = ∆t tf - ti

19. A. Speed & Velocity • Instantaneous Speed • speed at a given instant • Average Speed

20. A. Speed & Velocity • Problem: • A storm is 10 km away and is moving at a speed of 60 km/h. Should you be worried? • It depends on the storm’s direction!

21. A. Speed & Velocity • Velocity • speed in a given direction • can change even when the speed is constant!

22. A. Speed & Velocity • Velocity can be positive or negative • The sign of the average velocity depends upon the chosen coordinate system • Notice where the origin (reference point) is designated

23. d t v B. Calculations • Your neighbor skates at a speed of 4 m/s. You can skate 100 m in 20 s. Who skates faster? GIVEN: d = 100 m t = 20 s v = ? WORK: v = d ÷ t v = (100 m) ÷ (20 s) v = 5 m/s You skate faster!

24. d t v B. Calculations • Sound travels 330 m/s. If a lightning bolt strikes the ground 1 km away from you, how long will it take for you to hear it? GIVEN: v = 330 m/s d = 1km = 1000m t = ? WORK: t = d ÷ v t = (1000 m) ÷ (330 m/s) t = 3.03 s

25. B. Calculations • 1. Heather and Matthew take 34 min to walk eastward along a straight road to a store 2.0 km away. What is their average velocity in m/s • 2. Eugene is 75.0 km due south of Salem. If Joe rides from Salem to Eugene on his bike in 6.00 h, what is his average velocity? • 3. If the bus stop is 0.68 km down the street from the museum and it takes you 9.5 min to walk north from the bus stop to the museum entrance, what is your average velocity? • 4. Simpson drives his car with an average velocity of 24 m/s toward the east. How long will it take him to drive 560 km on a perfectly straight highway? • 5. How much time would Simpson save by increasing his average velocity to 26m/s east? • 6. A bus traveled south along a straight path for 3.2 h with an average velocity of 88 km/h, stopped for 20 min, then traveled south for 2.8 h with an average velocity of 75 km/h. • What is the average velocity for the total trip? • What is the displacement for the total trip?

26. Answers: • 1. 0.98 m/s to the east • 2. 12.5 km/h (3.47m/s) to the south • 3. 7.2 x 10-2 km/min (1.2 m/s) to the north • 4. 6.5 h • 5. 0.5 h • 6. a. 78 km/h to the south b. 490 km to the south

27. III. Acceleration

28. vf - vi t a A. Acceleration • Acceleration • the rate of change of velocity • change in speed or direction a: acceleration vf: final velocity vi: initial velocity t: time

29. A. Acceleration • Positive acceleration • “speeding up” • Negative acceleration • “slowing down”

30. vf - vi t a B. Calculations • A roller coaster starts down a hill at 10 m/s. Three seconds later, its speed is 32 m/s. What is the roller coaster’s acceleration? GIVEN: vi = 10 m/s t = 3 s vf = 32 m/s a = ? WORK: a = (vf- vi) ÷ t a = (32m/s - 10m/s) ÷ (3s) a = 22 m/s ÷ 3 s a= 7.3 m/s2

31. vf - vi t a B. Calculations • How long will it take a car traveling 30 m/s to come to a stop if its acceleration is -3 m/s2? GIVEN: t = ? vi = 30 m/s vf = 0 m/s a = -3 m/s2 WORK: t = (vf- vi) ÷ a t = (0m/s-30m/s)÷(-3m/s2) t = -30 m/s ÷ -3m/s2 t = 10 s

32. B. Calculations • 1. When the shuttle bus comes to a sudden stop to avoid hitting a dog, it slows from 9.00 m/s to 0.00 m/s in 1.50 s. Find the average acceleration of the bus. • 2. A car traveling initially at 7.0 m/s accelerates to a velocity of 12.0 m/s in 2.0 s. What is the average acceleration of the car? • 3. Turner’s treadmill starts with a velocity of -1.2 m/s and speeds up at regular intervals during a half hour workout. After 25 min, the treadmill has a velocity of -6.5 m/s. What is the average acceleration of the treadmill during this period?

33. B. Calculations • 4. If a treadmill starts with a velocity of -2.7 m/s and has a velocity of -1.3 m/s after 5.0 min, What is the average acceleration of the treadmill during this period? • 5. With an average acceleration of -0.50 m/s2, how long will it take a cyclist to bring a bicycle with an initial velocity of +13.5 m/s to a complete stop?

34. Answers • 1. -6 m/s2 • 2. 2.5 m/s2 • 3. -3.5 x 10-3 m/s2 • 4. 4.67 x 10-3 m/s2 • 5. 27 s

35. IV. Graphing Motion

36. Distance-Time Graph A B A. Graphing Motion • slope = • steeper slope = • straight line = • flat line = speed faster speed constant speed no motion

37. Distance-Time Graph A B A. Graphing Motion • Who started out faster? • A (steeper slope) • Who had a constant speed? • A • Describe B from 10-20 min. • B stopped moving • Find their average speeds. • A = (2400m) ÷ (30min) A = 80 m/min • B = (1200m) ÷ (30min) B = 40 m/min

38. Distance-Time Graph A. Graphing Motion • Acceleration is indicated by a curve on a Distance-Time graph. • Changing slope = changing velocity

39. Speed-Time Graph A. Graphing Motion • slope = • straight line = • flat line = acceleration • +ve = speeds up • -ve = slows down constant accel. no accel. (constant velocity)

40. Speed-Time Graph A. Graphing Motion Specify the time period when the object was... • slowing down • 5 to 10 seconds • speeding up • 0 to 3 seconds • moving at a constant speed • 3 to 5 seconds • not moving • 0 & 10 seconds