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Chapter 2 Motion Along a Straight Line

Chapter 2 Motion Along a Straight Line. Linear motion In this chapter we will consider moving objects: Along a straight line With every portion of an object moving in the same direction and at the same rate (particle-like motion). Types of physical quantities

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Chapter 2 Motion Along a Straight Line

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  1. Chapter 2 Motion Along a Straight Line

  2. Linear motion • In this chapter we will consider moving objects: • Along a straight line • With every portion of an object moving in the same direction and at the same rate (particle-like motion)

  3. Types of physical quantities • In physics, quantities can be divided into such general categories as scalars, vectors, matrices, etc. • Scalars – physical quantities that can be described by their value (magnitude) only • Vectors – physical quantities that can be described by their value and direction

  4. Distance, position, and displacement • Distance (scalar) a total length of the path traveled regardless of direction (SI unit: m) • In each instance we choose an origin – a reference point, convenient for further calculations • Position of an object (vector) is described by the shortest distance from the origin and direction relative to the origin • Displacement (vector) – a change from position xi to position xf

  5. Velocity and speed • Average speed (scalar) - a ratio of distance traveled (over a time interval) to that time interval (SI unit: m/s) • Average velocity (vector) - a ratio of displacement (over a time interval) to that time interval • Instantaneous velocity (vector) – velocity at a given instant • Instantaneous speed (scalar) – a magnitude of an instantaneous velocity

  6. Velocity and speed

  7. Velocity and speed

  8. Instantaneous velocity • The instantaneous velocity is the slope of the line tangent to the x vs. t curve • This would be the green line • The light blue lines show that as Δt gets smaller, they approach the green line

  9. Acceleration • Average acceleration (vector) - a ratio of change of velocity (over a time interval) to that time interval (SI unit = (m/s)/s = m/s2) • Instantaneous acceleration (vector) – a rate of change of velocity at a given instant

  10. Acceleration • The slope (green line) of the velocity-time graph is the acceleration • The blue line is the average acceleration

  11. Chapter 2 Problem 15 An object moves along the x axis according to the equation x(t) = (3.00 t2 - 2.00 t + 3.00) m, where t is in seconds. Determine (a) the average speed between t = 2.00 s and t = 3.00 s, (b) the instantaneous speed at t = 2.00 s and at t = 3.00 s, (c) the average acceleration between t = 2.00 s and t = 3.00 s, and (d) the instantaneous acceleration at t = 2.00 s and t = 3.00 s.

  12. Case of constant acceleration • Average and instantaneous accelerations are the same • Conventionally • Then

  13. Case of constant acceleration • Average and instantaneous accelerations are the same • Conventionally • Then

  14. Case of constant acceleration

  15. Case of constant acceleration

  16. Case of constant acceleration To help you solve problems

  17. Chapter 2 Problem 28 A particle moves along the x axis. Its position is given by the equation x = 2 + 3t - 4t2, with x in meters and t in seconds. Determine (a) its position when it changes direction and (b) its velocity when it returns to the position it had at t = 0.

  18. Case of free-fall acceleration • At sea level of Earth’s mid-latitudes all objects fall (in vacuum) with constant (downward) acceleration of • a = - g ≈ - 9.8 m/s2≈ - 32 ft/s2 • Conventionally, free fall is along a vertical (upward) y-axis

  19. Chapter 2 Problem 38 A ball is thrown directly downward, with an initial speed of 8.00 m/s, from a height of 30.0 m. After what time interval does the ball strike the ground?

  20. Alternative derivation Using definitions and initial conditions we obtain

  21. Graphical representation

  22. Graphical representation

  23. Graphical representation

  24. Graphical representation

  25. Graphical representation

  26. Graphical representation

  27. Graphical representation

  28. Graphical representation

  29. Graphical representation

  30. Graphical integration

  31. Graphical integration

  32. Answers to the even-numbered problems Chapter 2 Problem 4: (a) 50.0 m/s (b) 41.0 m/s

  33. Answers to the even-numbered problems • Chapter 2 • Problem 6: • 27.0 m • 27.0 m + (18.0 m/s)∆t + (3.00 m/s2)(∆t)2 • 18.0 m/s

  34. Answers to the even-numbered problems Chapter 2 Problem 12: (b) 1.60 m/s2; 0.800 m/s2

  35. Answers to the even-numbered problems • Chapter 2 • Problem 20: • 6.61 m/s • −0.448 m/s2

  36. Answers to the even-numbered problems Chapter 2 Problem 38: 1.79 s

  37. Answers to the even-numbered problems Chapter 2 Problem 48: (b) 3.00 × 10−3 s (c) 450 m/s (d) 0.900 m

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