1. Velocity-Time Graphs SNC2D – Physics M. M. Couturier

2. Velocity-Time Graphs As the term suggests, a velocity-time graph is a graph where velocity is plotted on the y-axis and time is plotted on the x-axis. As the term suggests, a velocity-time graph is a graph where velocity is plotted on the y-axis and time is plotted on the x-axis.

3. Velocity-Time Graphs Since acceleration is related to velocity and time (m/s 2 ), the slope of the function will reveal the average acceleration. Since acceleration is related to velocity and time (m/s 2 ), the slope of the function will reveal the average acceleration.

4. Velocity-Time Graphs As we did with position-time graphs, we need to understand the nature of the acceleration; so we must understand all four kinds of slopes: increasing, decreasing, and zero (within this new context). As we did with position-time graphs, we need to understand the nature of the acceleration; so we must understand all four kinds of slopes: increasing, decreasing, and zero (within this new context).

5. Velocity-Time Graphs This is an example of a zero slope. The change in velocity here is ∆v = 0 over a period of time, t. The average acceleration is therefore: This is an example of a zero slope. The change in velocity here is ∆v = 0 over a period of time, t. The average acceleration is therefore: a avg = ∆v = 0 = 0 a avg = ∆v = 0 = 0 ∆t t ∆t t Essentially, the object is traveling at a constant velocity. Essentially, the object is traveling at a constant velocity.

6. Velocity-Time Graphs This is an example of an increasing slope. ∆v and ∆t are both positive and therefore, a avg will also be positive. Also, since it is a straight line (linear), the acceleration is constant, meaning the acceleration is the same. This is an example of an increasing slope. ∆v and ∆t are both positive and therefore, a avg will also be positive. Also, since it is a straight line (linear), the acceleration is constant, meaning the acceleration is the same.

7. Velocity-Time Graphs This is an example of a decreasing slope. ∆v is negative and since ∆t can only be positive, a avg will be negative. They are slowing down. This is an example of a decreasing slope. ∆v is negative and since ∆t can only be positive, a avg will be negative. They are slowing down.

8. Velocity-Time Graphs Use this as an easy reference guide!!! Use this as an easy reference guide!!!

9. Velocity-Time Graphs Use this as an easy reference guide!!! Use this as an easy reference guide!!!

10. Velocity-Time Graphs Velocity-Time Graphs In order to calculate the average acceleration using a velocity-time graph, you need to isolate two points on a single line. Look at the velocity-time graph below and write down the coordinates of any two points on the line. In order to calculate the average acceleration using a velocity-time graph, you need to isolate two points on a single line. Look at the velocity-time graph below and write down the coordinates of any two points on the line.

11. Velocity-Time Graphs Velocity-Time Graphs Since the average acceleration is defined by: Since the average acceleration is defined by: a avg = ∆v a avg = ∆v ∆t ∆t The two points that we have selected provide both ∆v and ∆t. The two points that we have selected provide both ∆v and ∆t.

12. Velocity-Time Graphs Velocity-Time Graphs Lets say that you selected (t,v) as (4,8) and (0,0). Your ∆v = (8-0) and your ∆t = (4-0), hence; Lets say that you selected (t,v) as (4,8) and (0,0). Your ∆v = (8-0) and your ∆t = (4-0), hence; a avg = ∆v = (8 – 0) = 8 a avg = ∆v = (8 – 0) = 8 ∆t (4-0) 4 ∆t (4-0) 4 a avg = 2 m/s a avg = 2 m/s Does it matter which Does it matter which point you choose? point you choose?

13. Velocity-Time Graphs Velocity-Time Graphs Lets say that you selected (t,v) as (2,4) and (1,2). Your ∆v = (4-2) and your ∆t = (2-1), hence; Lets say that you selected (t,v) as (2,4) and (1,2). Your ∆v = (4-2) and your ∆t = (2-1), hence; a avg = ∆v = (4 – 2) = 2 a avg = ∆v = (4 – 2) = 2 ∆t (2-1) 1 ∆t (2-1) 1 a avg = 2 m/s a avg = 2 m/s Does it matter which Does it matter which point you choose? It does not matter!!! point you choose? It does not matter!!!

14. Velocity-Time Graphs Again, never hesitate to draw on the graph that is provided to you in the following manner. Again, never hesitate to draw on the graph that is provided to you in the following manner.

15. Velocity-Time Graphs Okay; lets describe qualitatively what is happening in each of these situations. Okay; lets describe qualitatively what is happening in each of these situations.

16. Velocity-Time Graphs Red car: Notice that the red car is moving at a constant velocity. It is therefore not accelerating. Red car: Notice that the red car is moving at a constant velocity. It is therefore not accelerating.

17. Velocity-Time Graphs Green car: Notice that the green car is increasing in velocity and is therefore accelerating. It is taking much more time to accelerate than the blue car, but it will eventually pass the red car. Green car: Notice that the green car is increasing in velocity and is therefore accelerating. It is taking much more time to accelerate than the blue car, but it will eventually pass the red car.

18. Velocity-Time Graphs Blue car: The blue car is also increasing in velocity and is therefore accelerating. It is accelerating at a faster rate than the green car. Blue car: The blue car is also increasing in velocity and is therefore accelerating. It is accelerating at a faster rate than the green car.

19. Review of position-time graphs Which graph goes with which car? Which graph goes with which car?

20. Review of position-time graphs Which graph goes with which car? Which graph goes with which car? B C A

21. Lets bring it all together!!! Watch the graphs and the cars!!! Watch the graphs and the cars!!!

22. Lets bring it all together!!!

23. The blue dot is being displaced equally each unit of time; ergo it is moving at a constant velocity, ergo, it is not accelerating! The blue dot is being displaced equally each unit of time; ergo it is moving at a constant velocity, ergo, it is not accelerating!

24. Lets bring it all together!!!

25. The blue dot is being displaced equally each unit of time; ergo it is moving at a constant velocity, ergo, it is not accelerating! The blue dot is being displaced equally each unit of time; ergo it is moving at a constant velocity, ergo, it is not accelerating!

26. Lets bring it all together!!!

27. The displacement of the blue dot is larger after each unit of time. It is therefore increasing in velocity, which is increasing equally each unit of time; ergo it is accelerating at a constant rate. The displacement of the blue dot is larger after each unit of time. It is therefore increasing in velocity, which is increasing equally each unit of time; ergo it is accelerating at a constant rate.

28. Lets bring it all together!!!

29. The displacement of the blue dot is smaller after each unit of time. It is therefore decreasing in velocity, which is decreasing equally each unit of time; ergo it is accelerating at a negative constant rate. The displacement of the blue dot is smaller after each unit of time. It is therefore decreasing in velocity, which is decreasing equally each unit of time; ergo it is accelerating at a negative constant rate.

30. Velocity-Time Graphs Task 1: Look at the graph below and determine the a average in each case and then write a short story to explain the events. Be creative. Task 1: Look at the graph below and determine the a average in each case and then write a short story to explain the events. Be creative.

31. Velocity-Time Graphs Task 2: Look at the graph below and determine the a average in each case and then write a short story to explain the events. Be creative. Task 2: Look at the graph below and determine the a average in each case and then write a short story to explain the events. Be creative.

32. Velocity-Time Graphs Lets do a test: Lets do a test: http://www.explorelearning.com/index.cfm?metho d=cResource.dspView&ResourceID=301 http://www.explorelearning.com/index.cfm?metho d=cResource.dspView&ResourceID=301 http://www.explorelearning.com/index.cfm?metho d=cResource.dspView&ResourceID=301 http://www.explorelearning.com/index.cfm?metho d=cResource.dspView&ResourceID=301