Understanding Motion: Velocity, Speed, and Reference Frames

1. Chapter 3 Describing Motion

2. Chapter Objectives • Describe a frame of reference • Define and calculate average velocity • Draw & interpret position vs. time graphs illustrating motion. • Differentiate between vectors and scalars. • Use average velocity equation to solve motion problems involving v, d and t • Differentiate between average velocity and instantaneous velocity. • Be able to determine the slope of a position-time graph and calculate velocity

4. What is motion? • How do you know something is moving? • What evidence do you need to be convinced that something is moving?

5. 4.1Motion Is Relative An object is moving if its position relative to a fixed point (reference point) is changing.

6. 4.1Motion Is Relative Even things that appear to be at rest move. When we describe the motion of one object with respect to another, we say that the object is moving relative to the other object. • A book that is at rest, relative to the table it lies on, is moving at about 30 kilometers per second relative to the sun. • The book moves even faster relative to the center of our galaxy.

7. 4.1Motion Is Relative The racing cars in the Indy 500 move relative to the track.

8. 4.1Motion Is Relative When we discuss the motion of something, we describe its motion relative to something else. • The space shuttle moves at 8 kilometers per second relative to Earth below. • A racing car in the Indy 500 reaches a speed of 300 kilometers per hour relative to the track. • Unless stated otherwise, the speeds of things in our environment are measured relative to the surface of Earth.

9. 4.1Motion Is Relative Although you may be at rest relative to Earth’s surface, you’re moving about 100,000 km/h relative to the sun.

10. 4.1Motion Is Relative think! A hungry mosquito sees you resting in a hammock in a 3-meters-per-second breeze. How fast and in what direction should the mosquito fly in order to hover above you for lunch?

11. 4.1Motion Is Relative think! A hungry mosquito sees you resting in a hammock in a 3-meters-per-second breeze. How fast and in what direction should the mosquito fly in order to hover above you for lunch? Answer:The mosquito should fly toward you into the breeze. When above you it should fly at 3 meters per second in order to hover at rest above you.

12. 4.1Motion Is Relative How can you tell if an object is moving?

13. 4.2Speed You can calculate the speed of an object by dividing the distance covered by time.

14. 4.2Speed Before the time of Galileo, people described moving things as simply “slow” or “fast.” Such descriptions were vague. Galileo is credited as being the first to measure speed by considering the distance covered and the time it takes. Speed is how fast an object is moving.

15. 4.2Speed Any combination of units for distance and time that are useful and convenient are legitimate for describing speed: • miles per hour (mi/h) • kilometers per hour (km/h) • centimeters per day • light-years per century

16. 4.2Speed A cheetah is the fastest land animal over distances less than 500 meters and can achieve peak speeds of 100 km/h.

17. 4.2Speed We will primarily use the unit meters per second (m/s) for speed. If a cheetah covers 50 meters in a time of 2 seconds, its speed is 25 m/s.

18. 4.2Speed

19. 4.2Speed Instantaneous Speed A car does not always move at the same speed. You can tell the speed of the car at any instant by looking at the car’s speedometer. The speed at any instant is called the instantaneous speed.

20. 4.2Speed The speedometer gives readings of instantaneous speed in both mi/h and km/h.

21. 4.2Speed Average Speed In a trip by car, the car will certainly not travel at the same speed all during the trip. The driver cares about the average speed for the trip as a whole. The average speed is the total distance covered divided by the time.

22. 4.2Speed Average speed can be calculated easily: For example, a distance of 240 kilometers during a time of 4 hours is an average speed of 60 km/h:

23. 4.2Speed The average speed is often quite different from the instantaneous speed. Whether we talk about average speed or instantaneous speed, we are talking about the rates at which distance is traveled.

24. 4.2Speed If we know average speed and travel time, the distance traveled is easy to find. total distance covered = average speed × travel time For example, if your average speed is 80 kilometers per hour on a 4-hour trip, then you cover a total distance of 320 kilometers.

25. 4.2Speed think! If a cheetah can maintain a constant speed of 25 m/s, it will cover 25 meters every second. At this rate, how far will it travel in 10 seconds? In 1 minute?

26. 4.2Speed think! If a cheetah can maintain a constant speed of 25 m/s, it will cover 25 meters every second. At this rate, how far will it travel in 10 seconds? In 1 minute? Answer:In 10 s the cheetah will cover 250 m, and in 1 min (or 60 s) it will cover 1500 m.

27. 4.2Speed think! The speedometer in every car also has an odometer that records the distance traveled. If the odometer reads zero at the beginning of a trip and 35 km a half hour later, what is the average speed?

28. 4.2Speed think! The speedometer in every car also has an odometer that records the distance traveled. If the odometer reads zero at the beginning of a trip and 35 km a half hour later, what is the average speed? Answer:

29. 4.2Speed How can you calculate speed?

30. Motion Diagrams • What can you determine about the motion of the bird? The runner? The car?

31. A. Picturing Motion • 1. Motion diagram - series of images of a moving object that records its position after equal time intervals • used to describe object at rest, in constant motion, accelerating, decelerating • 2. Particle Model • a. replace object with a single point • b. point is usually center of mass of object • c. object is << than distance moved

32. Particle Diagram

33. B. Where and When • 1. Coordinate System • a. tells you where the zero point is for the variable being studied • b. provides directions for increase/decrease • 2. Position Vector • an arrow, showing magnitude and direction

34. Coordinate Systems • Indicate direction

35. Distance vs. Displacement • A jogger travels 2 km, stops to rest, then jogs back to his starting place. • What is the distance the jogger traveled? • What is his displacement?

36. b. Displacement(position) vs Distance • (1) Displacement - separation, length and direction, from an object’s starting point and its final location • a vector quantity • (2) Distance - how much, how large a separation exists • a scalar quantity, length of the arrow

37. Displacement • ∆d = df - di

38. Motion • Displacement is the distance and direction of an object's change in position from a reference point. • Suppose a runner jogs to the 50-m mark and then turns around and runs back to the 20-m mark. • The runner travels 50 m in the original direction (north) plus 30 m in the opposite direction (south), so the total distance she ran is 80 m.

39. Time Intervals • ∆t

40. c. Time Interval • (1) ti, pronounced t initial, is used to describe time at start point • (2) tf would be the final time at end point • (3) change in a quantity is represented by the Greek letter delta, D • (a) change is always final minus initial • (b) change in time is, Dt = tf - ti • (c) change in displacement Dd = df - di

41. What is the runners average velocity? _ V = Dd/Dt = 50m-0m/6s-0s = 50m/6s = 8.3 m/s

42. Position-Time Graphs

43. Position Time Graph • A plot of displacement over period of time: • Eq: d = v t, d is dependent, t is independent, v is constant • What is the slope of this line? • slope = change in displacement over time • in other words - ??

44. Position vs. Time Graphs • What does the slope of a position-time graph tell us? • The velocity • slope = m/s

45. 1. When finding the slope use the largest possible triangle for greater precision • 2. The line goes through origin only if initial displacement was zero at time t = 0

46. 4.3Velocity Speed is a description of how fast an object moves; velocity is how fast and in what direction it moves.

47. 4.3Velocity In physics, velocity is speed in a given direction. • When we say a car travels at 60 km/h, we are specifying its speed. • When we say a car moves at 60 km/h to the north, we are specifying its velocity.

48. 4.3Velocity A quantity such as velocity that specifies direction as well as magnitude is called a vector quantity. • Speed is a scalar quantity. • Velocity, like displacement, is a vector quantity.

49. 4.3Velocity Constant Velocity Constant speed means steady speed. Something with constant speed doesn’t speed up or slow down. Constant velocity means both constant speed and constant direction. Constant direction is a straight line, so constant velocity means motion in a straight line at constant speed. Can an object in orbit around the Earth be traveling at a constant velocity??

50. 4.3Velocity Changing Velocity If either the speed or the direction (or both) is changing, then the velocity is changing. • Constant speed and constant velocity are not the same. • A body may move at constant speed along a curved path but it does not move with constant velocity, because its direction is changing every instant.