Motion in One Dimension

1. Motion in One Dimension Chapter 2 Holt Physics

2. 2-1 Displacement and Velocity • Essential Questions / Concepts • Describe motion in terms of frame of reference, displacement, time, and velocity. • Calculate the displacement of an object traveling at a known velocity for a specific time interval. • Construct and interpret graphs of position versus time.

3. One Dimensional Motion • One dimensional motion is the simplest form. • It is motion that only takes place in a straight line. • In can include motion in two directions (left and right, forward and back…)

4. Frame of Reference • One must choose a frame of reference to describe any form of motion. • If an object is at rest (not moving), its position does not change with respect to the frame of reference. • Any frame of reference will do as long as we are consistent.

5. Displacement • The length of a straight line drawn from an object’s initial position to its final position. • Displacement = change in position = Final position – initial position Δx = xf– xi

7. Displacement • Displacement is not always equal to the distance traveled. • Displacement can be positive or negative. • Unless otherwise stated, movement to the right or upward movement will be considered positive • Movement to the left or downward movement will be considered negative.

9. Velocity • Average velocity is displacement divided by the time interval. • The unit of velocity is meters per second, or m/s Δxxf - xi V avg= = Δttf - ti

10. Average Velocity • Average velocity can be either positive or negative depending on the sign of the displacement. • Average velocity is equal to the constant velocity needed to cover the displacement in the given time interval.

11. Problems: Page 44 #1 Heather and Matthew walk eastward with a speed of 0.98 m/s. If it takes the 34 minutes to walk to the store, how far have they walked?

12. North = 0 Degrees or 360 Degrees West = 270 Degrees East = 90 Degrees South = 180 Degrees

13. Problems: Page 44 #2 If Joe rides south on his bicycle in a straight line for 15 minutes with an average speed of 12.5 km/h, how far has he riden?

14. Problems: Page 44 #3 It takes you 9.5 min to walk with an average velocity of 1.2 m/s to the north from the bus stop to the museum entrance. What is your displacement?

15. Problems: Page 44 #4 Simpson drives his car with an average velocity of 48.0 km/h to the east. How long will it take him to drive 144 km on a straight highway?

16. Problems: Page 44 #5 Look back at item #4. How much time would Simpson save by increasing his average velocity to 56.0 km/h to the east?

17. Problems: Page 44 #6 A bus travels 280 km south along a straight path with an average velocity of 88 km/h to the south. The bus stops for 24 min, then it travels 210 km south with an average velocity of 75 km/h to the south. a) How long does the total trip last? b) What is the average velocity for the total trip?

18. Velocity vs Speed • Velocity describes motion with both a direction and a numerical value (a magnitude). • Speed has no direction, only a magnitude.

19. Interpreting Velocity Graphically • Velocity is a graph of change in position vs change in time. • Position is on the y-axis while time is on the x-axis. • The slope of the line (rise over run) is equal to the velocity (meters per second).

21. Graphing Velocity Object #2 Object #1 Position (m) Object #3 Time (s)

22. Average vs Instantaneous Velocity Describe the average velocity: Position (m) Where is average velocity equal to Instantaneous velocity? Time (s)

23. Average vs Instantaneous Velocity Describe the average velocity: Position (m) Where is average velocity equal to Instantaneous velocity? Time (s)

24. Average vs Instantaneous Velocity • Instantaneous velocity may not be the same as the average velocity. • To determine instantaneous velocity we must consider a small (VERY small) time interval. • A straight line that is TANGENT to the curve of velocity indicates instantaneous velocity.

25. Consider Problem 3 on Page 47 Position (m) Time (s)

26. Number 5, Page 47 • An athlete swims from the north end to the south end of a 50.0 m pool in 20.0 s and makes the return trip to the starting position in 22.0 s. • What is the average velocity of the first half? • What is the average velocity for the second half? • What is the average velocity for the round trip?

27. Number 6, Page 47 • Two students walk in the same direction along a straight path, at a constant speed – one at 0.90 m/s and the other at 1.90 m/s. • Assuming that they start at the same point at the same time, how much sooner does the faster student arrive at a destination 780 m away? • How far would the student have to walk so that the faster student arrives 5.50 min before the slower student?

28. 2-2 Acceleration • Essential Questions / Concepts: • Describe motion in terms of changing velocity. • Compare graphical representations of accelerated and non-accelerated motions. • Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration.

29. Changes in Velocity • Acceleration measures the rate of change in velocity. • What is on the x-axis of any graph of a rate? • A graph of acceleration is a graph of velocity over time (meters per second, per second).

30. Acceleration • Average acceleration is velocity divided by the time interval. • The unit of acceleration is meters per second per second , or m/s2 Δvvf - vi aavg= = Δttf - ti

31. Problems 1-5 on Page 49 • Homework assignment – you MUST show your work!

32. Changes in Velocity • Acceleration has both direction and magnitude. • When the Δv is positive, the acceleration is positive. • When the velocity is constant, the acceleration is equal to zero.

33. Changes in Velocity • Imagine a train, traveling in a positive direction, slows down as it approaches the next station. • Is the acceleration positive or negative? • Acceleration is final velocity minus initial velocity, so the Δv will be negative and the Δa will be negative even though the velocity is always positive.

34. Slope and Shape of Graph of Motion Describe in detail the motion at each of the three marked points

35. Motion with Constant Acceleration

36. Velocity vs Time (Acceleration) for Giancarlo Fiscichella at Melbourne, Australia

38. Displacement • Displacement depends on acceleration, initial velocity, and time. • The area under the curve in a graph of velocity versus time equals the displacement.

39. Equation for Displacement with Constant Acceleration Look at the sample problem on page 53… Do Problems 1-5 on page 53 for homework.

40. Final Velocity • Final velocity depends on initial velocity, acceleration, and time. • By rearranging the equation for acceleration, we can find a value for the final velocity.

41. Equation for Final Velocity with Constant Acceleration

42. Another Equation for Displacement with Constant Acceleration Look at the sample problem on page 55… Do Problems 1-4 on page 55 for homework.

43. Equation for Final Velocity

45. 2-3 Falling Objects • Essential Questions / Concepts • Relate the motion of a freely falling body to motion with constant acceleration. • Calculate displacement, velocity, and time at various points in the motion of a freely falling object. • Compare the motions of different objects in free fall

46. Free Fall • It has been demonstrated that in the absence of air resistance all objects fall with the same constant acceleration. • Free fall acceleration is denoted by the symbol g. • The acceleration of all objects near the earth’s surface is approximately 9.81 m/s2.

48. Constant Free Fall Acceleration The graph indicates constant acceleration at every moment

49. To Summarize Motion

50. Homework Problems • Students should understand and be able to answer the Review Questions from each section on pages 69-72. • From the Chapter 3 Review and Assess section beginning on page 69 do problem numbers 8, 10, 14, 20, 24, 26, 30,38, 40, and 42. • Bonus Questions for Extra Credit: number 45, 46, 55 and 56.