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Position-Time and Velocity-Time Graphs

Position-Time and Velocity-Time Graphs. Position-Time Graphs Review. What information does the slope on a P-T Graph show you?. 50. change in y. slope =. 40. change in x. 30. position (m). (30 m – 10 m). 20. slope =. (30 s – 0 s). 10. (20 m). 10. 20. 30. 40. slope =. (30 s).

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Position-Time and Velocity-Time Graphs

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  1. Position-Time and Velocity-Time Graphs

  2. Position-Time Graphs Review • What information does the slope on a P-T Graph show you?

  3. 50 change in y slope = 40 change in x 30 position (m) (30 m – 10 m) 20 slope = (30 s – 0 s) 10 (20 m) 10 20 30 40 slope = (30 s) time (s) Position-Time Graphs • The slope of a P-T graph is equal to the object’s velocity in that segment. slope = 0.7 m/s

  4. 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 9 10 8 Position-Time Graphs position (cm) time (s)

  5. 10 9 8 7 6 5 position (cm) 4 3 2 1 time (s) 1 2 3 4 5 6 7 9 10 8 Position-Time Graphs • What are the characteristics of this graph? • Diagonal line, positive slope • What kind of motion created this graph? • Constant velocity

  6. Position-Time Graphs • Each type of motion has a characteristic shape on a P-T graph. • Constant speed • Zero speed (at rest) • Accelerating (speeding up) • Decelerating (slowing down)

  7. time (s) time (s) pos. (m) pos. (m) Constant speed in positive direction. Moving away from 0 Constant speed in negative direction. Moving toward zero Position-Time Graphs • Constant velocity is represented by a diagonal line on the P-T graph.

  8. time (s) pos. (m) A horizontal segment means the object is at rest. Position-Time Graphs • At Rest is represented by a horizontal line on the P-T graph.

  9. time (s) time (s) pos. (m) pos. (m) Speeding up in positive direction. Speeding up in negative direction. Position-Time Graphs • Curved segments on the P-T graph mean the object’s speed is changing.

  10. time (s) time (s) pos. (m) pos. (m) Traveling in positive direction, but slowing down. Traveling in negative direction, but slowing down. Position-Time Graphs • Curved segments on the P-T graph mean the object’s speed is changing.

  11. 50. change in y slope = 40. change in x velocity (m/s) 30. (50. m/s – 10. m/s 20. slope = (3.0 s – 0 s) 10. (40. m/s) 1.0 2.0 3.0 4.0 slope = (3.0 s) time (s) Velocity -Time Graphs • The slope of a V-T graph is equal to the object’s acceleration in that segment. slope = 13 m/s2

  12. + velocity (m/s) time (s) - Velocity-Time Graphs • This Graph shows an object moving with a constant positive velocity, but No Acceleration Object is moving with a constant velocity in the (+) direction

  13. + velocity (m/s) time (s) - Velocity-Time Graphs • This graph shows an object moving with a constant negative velocity, but no acceleration Object is moving with a constant velocity in (-) direction

  14. + velocity (m/s) time (s) - Velocity-Time Graphs • This graph shows an object not moving. Object is at rest

  15. Acceleration is a Vector • Because acceleration is a vector, we also have to include a direction. • Acceleration is a vector that points in the same direction as the change in velocity. • Therefore; the direction of acceleration is determined by the direction of the slope.

  16. + + velocity (m/s) velocity (m/s) time (s) time (s) The direction of the slope indicates whether acceleration is positive or negative: This object is speeding up in the positive direction This object has a positive slope; therefore a positive acceleration. This object is slowing down in the negative direction - - Velocity-Time Graphs • V-T Graphs that show Positive Accelerations

  17. + + velocity (m/s) velocity (m/s) time (s) time (s) This object has a negative slope; therefore acceleration will be negative. Object is slowing down in the positive direction This object has a negative slope; therefore acceleration will be negative. object is speeding up in the negative direction - - Velocity-Time Graphs • V-T graphs that show Negative Accelerations

  18. Velocity-Time Graphs • A velocity-time (V-T) graph shows an object’s velocity as a function of time. • A horizontal line = constant velocity. • A straight sloped line = constant acceleration. • Acceleration = change in velocity over time. • Positive slope = positive acceleration. • Not necessarily speeding up! • Negative slope = negative acceleration. • Not necessarily slowing down!

  19. Checkpoint Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that are true): A. moving with positive velocity. B. moving with a constant velocity. C. moving with a negative velocity. D. slowing down. E. changing directions. F. speeding up. G. moving with a positive acceleration. H. moving with a negative acceleration

  20. ANSWER • A,D, and H

  21. RESEARCH • Explain how an object with a positive acceleration can be slowing down. • Explain how an object with a negative acceleration can be speeding up.

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