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Chapter 2 Motion in One Dimension

Chapter 2 Motion in One Dimension. Dynamics Dynamics : branch of physics describing the motion of an object and the relationship between that motion and other physics concepts

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Chapter 2 Motion in One Dimension

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  1. Chapter 2 Motion in One Dimension

  2. Dynamics • Dynamics: branch of physics describing the motion of an object and the relationship between that motion and other physics concepts • Kinematics is a part of dynamics. In kinematics we are interested in the description of motion, without the description of the cause of the motion • Any motion involves three concepts used to study objects in motion: • 1) Displacement • 2) Velocity • 3) Acceleration

  3. 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)

  4. 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

  5. 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

  6. 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

  7. Velocity and speed

  8. Velocity and speed

  9. 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

  10. 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

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

  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 To help you solve problems

  15. Case of constant acceleration

  16. Case of constant acceleration

  17. Graphical representation

  18. Graphical representation

  19. Graphical representation

  20. Graphical representation

  21. Graphical representation

  22. Graphical representation

  23. Graphical representation

  24. Graphical representation

  25. Graphical representation

  26. Chapter 2 Problem 36 A car accelerates uniformly from rest to a speed of 40.0 mi/h in 12.0 s. Find (a) the distance the car travels during this time and (b) the constant acceleration of the car.

  27. 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

  28. Chapter 2 Problem 45 A certain freely falling object requires 1.50 s to travel the last 30.0 m before it hits the ground. From what height above the ground did it fall?

  29. Questions?

  30. Answers to the even-numbered problems Chapter 2 Problem 4: 12.2 mi/h

  31. Answers to the even-numbered problems Chapter 2 Problem 8: (a) 2.3 min (b) 64 mi

  32. Answers to the even-numbered problems Chapter 2 Problem 16: (a) 41.0 m/s, 41.0 m/s, 41.0 m/s (b) 17.0 m/s, much less than the results of (b)

  33. Answers to the even-numbered problems Chapter 2 Problem 20: 0.75 m/s2

  34. Answers to the even-numbered problems Chapter 2 Problem 32: (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km

  35. Answers to the even-numbered problems Chapter 2 Problem 50: (a) 2.3 s (b) - 33 m/s

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