1. This lesson will teach you how to draw and analyze velocity time graphs. This lesson will teach you how to draw and analyze velocity time graphs. Many aspects of graphical analysis will also be covered Many aspects of graphical analysis will also be covered SPH 3U Grade 11 U Physics

2. By the end of this lesson, you will be able to: What are we going to cover today? v-t graphing basics SPH 3U Grade 11 U Physics Analyze uniform v-t graphs Analyze non - uniform v-t graphs Homework

7.  What is the distance?  What is the displacement?  What is the speed?  What is the velocity?  What are they in km/hr?  What is the acceleration? 82.5m 3s 1 sec Or 33 km/hr 2 sec Or 66 km/hr 3 sec Or 99 km/hr 99 - 0 3 - 0

8.  Velocity-time graph  A graph describing the motion of an object  Velocity = y-axis  Time = x-axis  Slope = average acceleration  Acceleration a  How quickly an objects velocity changes over time (rate of change)  vector

9. SPH 3U Grade 11 U Physics The slope of a v-t graph is acceleration, a The area under a v-t graph is displacement,  d

10. SPH 3U Grade 11 U Physics time (s) 7.0 velocity (m/s [U]) 6.0 5.0 3.0 4.0 1.0 2.0 1.02.03.04.05.06.07.0 Units of the slope are m/s/s or m/s 2 units of acceleration units of acceleration Area Units of the area are m units of displacement units of displacement

11. -2.0 0 1.0 2.0 3.0 4.0 11 12 13 14 -3.0 -4.0 velocity (m/s [E]) 1.0 2.03.0 4.05.0 6.0 7.0 8.09.010. time (s) SPH 3U Grade 11 U Physics accelerating east

12. -2.0 0 1.0 2.0 3.0 4.0 11 12 13 14 -3.0 -4.0 velocity (m/s [E]) 1.0 2.03.0 4.05.0 6.0 7.0 8.09.010. time (s) SPH 3U Grade 11 U Physics moving east at constant velocity

13. -2.0 0 1.0 2.0 3.0 4.0 11 12 13 14 -3.0 -4.0 velocity (m/s [E]) 1.0 2.03.0 4.05.0 6.0 7.0 8.09.010. time (s) SPH 3U Grade 11 U Physics accelerating west Or Neg. acceleration east

14. -2.0 0 1.0 2.0 3.0 4.0 11 12 13 14 -3.0 -4.0 velocity (m/s [E]) 1.0 2.03.0 4.05.0 6.0 7.0 8.09.010. time (s) SPH 3U Grade 11 U Physics moving west at constant velocity

15. -2.0 0 1.0 2.0 3.0 4.0 11 12 13 14 -3.0 -4.0 velocity (m/s [E]) 1.0 2.03.0 4.05.0 6.0 7.0 8.09.010. time (s) SPH 3U Grade 11 U Physics accelerating east

16. -2.0 0 1.0 2.0 3.0 4.0 11 12 13 14 -3.0 -4.0 velocity (m/s [E]) 1.0 2.03.0 4.05.0 6.0 7.0 8.09.010. time (s) SPH 3U Grade 11 U Physics The x-axis does not represent the origin The x-axis represents a velocity of zero

17. 1. What is the slope of a v-t graph? SPH 3U Grade 11 U Physics a.Displacement b.Velocity c.Acceleration d.Position e.None of the above

18. 2. What is the area under a v-t graph? SPH 3U Grade 11 U Physics a.Displacement b.Velocity c.Acceleration d.Position e.None of the above

19. SPH 3U Grade 11 U Physics 3. Which v-t graph depicts no motion? a. b. c.d.

20. time (s) 14 velocity (m/s [U]) 12 10. 6.0 8.0 2.0 4.0 1.02.03.04.05.06.07.0 time (s)velocity (m/s [U]) 0.010. 1.010. 2.010. 3.010. 4.010. 5.010. 6.01o. Since the accel is zero, the object has a constant velocity SPH 3U Grade 11 U Physics

21. Uniform motion is a horizontal line on a v-t graph time (s) 14 velocity (m/s [U]) 12 10. 6.0 8.0 2.0 4.0 1.02.03.04.05.06.07.0

22. time (s) 14 velocity(m/s [E]) 12 10. 6.0 8.0 2.0 4.0 1.02.03.0 time (s)velocity (m/s [E]) 0.0 1.04.0 2.08.0 3.012.0 Notice that the line is not curved. It is a diagonal line SPH 3U Grade 11 U Physics

23. time (s) 14 velocity (m /s [E]) 12 10. 6.0 8.0 2.0 4.0 1.02.03.0 SPH 3U Grade 11 U Physics

24. Curved velocity time graphs represent non-uniform acceleration and we will not be studying this type of motion in this class. To determine average speed from a v-t graph we use: To determine average vel from a v-t graph we use: To determine inst vel from a v-t graph we simply read the vel values on the graph

25. SPH 3U Grade 11 U Physics 4. Which v-t graph depicts an object moving at constant velocity? a. b. c.d.

26. Plot the velocity time data and answer the following SPH 3U Grade 11 U Physics time (s)velocity (m/s [N]) 0.05.0 1.010. 2.010. 3.05.0 4.00.0 5.0-5.0 6.0-5.0 7.00.0

27. 5. What is the accel of the object between 0 – 1 s? SPH 3U Grade 11 U Physics a.-2.0 m/s 2 [N] b.2.0 m/s 2 [N] c.5.0 m/s 2 [S] d.-5.0 m/s 2 [S]

28. 6. When is the object not moving? SPH 3U Grade 11 U Physics a.Between 1 and 2 s b.Between 5 and 6 s c.Both a and b d.at 4.0 s and 7.0 s e.The object never stops

29. 7. How long was the object stopped? SPH 3U Grade 11 U Physics a.1.0 s b.2.0 s c.5.0 s d.The object stops for only a brief moment e.The object never stops

30. 8. What is the objects displacement? SPH 3U Grade 11 U Physics a.5.0 m [N] b.18 m [N] c.5.0 m [S] d.33 m [N]

31. 9. What is the average speed of the object? SPH 3U Grade 11 U Physics a.2.6 m/s [S] b.2.6 m/s [N] c.5.4 m/s [S] d.5.4 m/s [N] e.None of the above

32. 10. What is the average velocity of the object? SPH 3U Grade 11 U Physics a.2.6 m/s [N] b.2.6 m/s [S] c.5.4 m/s [N] d.5.4 m/s [S] e.None of the above

33. SPH 3U Grade 11 U Physics Read pgs 21 – 35 Practice 1 & 2 on pg 29 Questions 1-4 on pg 35