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# Chapter 2

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### Chapter 2

1. 1. Motion in One Dimension<br />Chapter 2<br />Pg. 40-65<br />
2. 2. 2.1 Displacement and Velocity<br />
3. 3. What do you think?<br />Is the book on your instructor’s desk in motion?<br />Explain your answer.<br />What are some examples of motion?<br />How would you define motion?<br />
4. 4. One-Dimensional Motion<br />It is the simplest form of motion<br />This is motion that happens in one direction<br />Example:<br />Train on the tracts moving forward or backward<br />
5. 5. Displacement (x)<br />Change in position<br />Can be positive or negative<br />It describes the direction of motion<br />You will see me use d instead of xfor displacement<br />
6. 6. Displacement (x)<br />Displacement is not always equal to the distance traveled<br />A gecko runs up a tree from the 20 cm marker to the 80 cm marker, then he retreats to the 50 cm marker?<br />
7. 7. Displacement (x)<br />In total it traveled 90 cm, however, the displacement is only 30 cm<br />x or d= 50cm- 20cm = 30 cm<br />If the gecko goes back to the start<br />The displacement is zero<br />
8. 8. Displacement<br />What is the displacement for the objects shown?<br />Answer: 70 cm<br /><ul><li>Answer: -60 cm</li></li></ul><li>Displacement - Sign Conventions<br /><ul><li>Right (or east) ---> +</li></ul>Left (or west) ---> – <br />Up (or north) ----> +<br />Down (or south) ---> –<br />
9. 9. Average Velocity<br /><ul><li>Average velocity is displacement divided by the time interval.</li></ul>The total displacement divided by the time interval during which the displacement occurred (Vavg)<br />Basically velocity is distance/time<br />
10. 10. Average Velocity<br />The units can be determined from the equation.<br />SI Units: m/s<br />Other Possible Units: mi/h, km/h, cm/year<br />Velocity can be positive or negative but time must always be positive<br />
11. 11. Average Velocity<br />You travel 370 km west to a friends house. You left at 10am and arrived at 3pm. What was your average velocity?<br />Vavg = d = -370 km<br />Δt 5.0h<br />Vavg= -74 km/h or 74 km/h west<br />
12. 12. Classroom Practice Problems <br />Joey rides his bike for 15 min with an average velocity of 12.5 km/h, how far did he ride? <br />Vavg = d<br />Δt<br />d = (12.5 km/h) (0.25h)<br />d = 3.125 km<br />
13. 13. Speed<br />Speed does not include direction while velocity does.<br />Speed uses distance rather than displacement.<br />In a round trip, the average velocity is zero but the average speed is not zero. <br />
14. 14. Graphing Motion<br />How would you describe the motion shown by this graph?<br />Answer: Constant speed (straight line)<br />What is the slope of this line?<br />Answer: 1 m/s<br />What is the average velocity?<br />Answer: 1 m/s<br />
15. 15. Graphing Motion<br />Describe the motion of each object.<br />Answers<br />Object 1: constant velocity to the right or upward<br />Object 2: constant velocity of zero (at rest)<br />Object 3: constant velocity to the left or downward<br />
16. 16. 2.2 Acceleration<br />Pg. 48 to 59<br />
17. 17. What do you think?<br />Which of the following cars is accelerating?<br />A car shortly after a stoplight turns green<br />A car approaching a red light<br />A car with the cruise control set at 80 km/h<br />A car turning a curve at a constant speed<br />Based on your answers, what is your definition of acceleration?<br />
18. 18. Acceleration<br />What are the units?<br />SI Units: m/s2<br />Other Units: (km/h)/s or (mi/h)/s<br />Acceleration = 0 implies a constant velocity (or rest)<br />
19. 19. Classroom Practice Problem<br />A bus slows down with an average acceleration of -1.8m/s2. how long does it take the bus to slow from 9.0m/s to a complete stop?<br />Find the acceleration of an amusement park ride that falls from rest to a velocity of 28 m/s downward in 3.0 s.<br />9.3 m/s2 downward<br />
20. 20. Acceleration<br />Displacement with constant acceleration<br />d = ½ (vi + vf) Δt<br />Displacement= ½ (initial velocity + final velocity) (time)<br />
21. 21. Example<br />A racecar reaches a speed of 42m/s. it uses its parachute and breaks to stop 5.5s later. Find the distance that the car travels during breaking. <br />Given: vi = 42 m/s vf= 0 m/s<br />t = 5.5 sec d = ?? <br />
22. 22. Example<br />d = ½ (vi + vf) Δt<br />d = ½ (42+0) (5.5)<br />d = 115.5 m<br />
23. 23. Acceleration<br />Final velocity<br />Depends on initial velocity, acceleration and time<br />Velocity with constant acceleration<br />vf = vi + aΔt<br />Final velocity = initial velocity + (acceleration X time)<br />
24. 24. Acceleration<br />Displacement with constant acceleration<br />d = viΔt + ½ a (Δt)2<br />Displacement = (initial velocity X time) + ½ acceleration X time2<br />
25. 25. Example<br />A plane starting at rest at one end of a runway undergoes uniform acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at takeoff? How long must the runway before the plane to be able to take off?<br />Given: vi = 0 m/s a= 4.8m/ss<br />t= 15s vf = ?? d= ??<br />
26. 26. Example<br />What do we need to figure out?<br />Speed at takeoff<br />How long the runway needs to be<br />vf = vi + aΔt<br />vf = 0m/s + (4.8 m/s2)(15 s)<br />vf = 72m/s<br />
27. 27. Example<br />d = viΔt + ½ a (Δt)2<br />d = (0m/s)(15s) + ½ (4.8m/s2)(15s)2<br />d = 540 m<br />
28. 28. Acceleration<br />Final velocity after any displacement<br />vf2 = vi2 +2ad<br />Final velocity2 = initial velocity2 + 2(acceleration)(displacement)<br />
29. 29. Example<br />An aircraft has a landing speed of 83.9 m/s. The landing area of an aircraft carrier is 195 m long. What is the minimum uniform acceleration required for safe landing?<br />Answer: -18.0 m/s2<br />
30. 30. Useful Equations<br />1.<br />2.<br />3.<br />4.<br />5.<br />d = 1 (vi + vf) t<br /> 2<br />
31. 31. Classroom Practice Problems<br />A bicyclist accelerates from 5.0 m/s to 16 m/s in 8.0 s. Assuming uniform acceleration, what distance does the bicyclist travel during this time interval?<br />Answer: 84 m<br />
32. 32. 2.3 Falling Objects<br />
33. 33. Free Fall<br />The motion of a body when only the force due to gravity is acting<br />Acceleration is constant for the entire fall<br />Acceleration due to gravity (ag or g)<br />Has a value of -9.81 m/s2 (we will use 10m/s2)<br />Negative for downward<br />Roughly equivalent to -22 (mi/h)/s<br />
34. 34. Free Fall<br />Acceleration is constant during upward and downward motion<br />Objects thrown into the air have a downward acceleration as soon as they are released. <br />
35. 35. Free Fall<br />The instant the velocity of the ball is equal to 0 m/s is the instant the ball reaches the peak of its upward motion and is about to begin moving downward.<br />REMEMBER!!! <br />Although the velocity is 0m/s the acceleration is still equal to 10 m/s2<br />
36. 36. Example<br />Jason hits a volleyball so that it moves with an initial velocity of 6m/s straight upward. If the volleyball starts from 2.0m above the floor how long will it be in the air before it strikes the floor?<br />We want to use our velocity and acceleration equations<br />
37. 37. Example<br />Given: vi = 6m/s a= 10m/s2<br />d= -2.0m t = ?? vf = ??<br />vf2= vi2 + 2ad<br />vf= at + vi<br />
38. 38. Free Fall<br />For a ball tossed upward, make predictions for the sign of the velocity and acceleration to complete the chart.<br />
39. 39. Graphing Free Fall<br />Based on your present understanding of free fall, sketch a velocity-time graph for a ball that is tossed upward (assuming no air resistance).<br />Is it a straight line?<br />If so, what is the slope?<br />Compare your predictions to the graph to the right.<br />
40. 40. Classroom Practice Problem<br />A ball is thrown straight up into the air at an initial velocity of 25.0 m/s upward. Create a table showing the ball’s position, velocity and acceleration each second for the first 5 s.<br />
41. 41. Direction of Acceleration<br />Describe the motion of an object with<br />vi and a as shown to the left.<br />Moving right as it speeds up<br />Moving right as it slows down<br />Moving left as it speeds up<br />Moving left as it slows down<br />
42. 42. Graphing Velocity<br />The slope (rise/run) of a velocity/time graph is the acceleration.<br />Rise is change in v<br />Run is change in t<br />This graph shows a constant acceleration.<br />Average speed is the midpoint.<br />
43. 43. Graph of v vs. t for a train<br />Describe the motion at points A, B, and C.<br />Answers<br />A: accelerating (increasing velocity/slope) to the right<br />B: constant velocity to the right<br />C: negative acceleration (decreasing velocity/slope) and still moving to the right<br />