1. What we will do today:
Revise graphs of motion (eg velocity time graphs)
Describe the motion of an acceleration-time (a-t) graph.
Draw a-t graphs from the information obtained from v-t graphs.

2. Velocity – time graphs
In your jotters / show-me boards draw the following v-t graphs:
Constant velocity.
Constant acceleration.
Constant decelaration.

3. Graphs of Motion

4. Note that in the following graphs,
a = acceleration
v = velocity
s = displacement
Just as the area under a speed-time graph gives the distance travelled,
The area under a velocity-time graph gives the displacement.

5. Graphs Showing Constant Accelerationv s t t t

6. Graphs Showing Constant Velocityt

7. Graphs Showing Constant Decelerationv s t t t

8. Example The following v-t graph is produced for a moving body:
Describe its movement at each point.
Draw the corresponding a-t graph (values must be included).

9. Solution (a) AB – const accn. from 0 – 10ms-1 in 2s.
BC – const vel. of 10ms-1 for 2s.
CD – const decn. from 10 – 0ms-1 in 1s.
DE – body is stationary for 3s.
EF - const accn. from 0 – 8ms-1 in 2s in opposite direction.
FG – const vel. of 8ms-1 for 3s in opposite direction.
GH – const decn. from 8 – 0ms-1 in 1s in opposite direction.

10. Solution (b) BC, DE, FG – all constant vel. therefore no accn.
Use a = v – u / t for all other accn.
AB: 10 – 0 / 2 = 5 ms-2
CD: 0 – 10 / 1 = - 10 ms-2
EF: -8 – 0 / 2 = - 4 ms-2
GH: 0- (-8) / 1 = 8 ms-2

11. Solution (b)

12. 2003 Qu: 2

13. 2009

14. 2008 Qu: 22(b)

15. 2008 Qu: 22(b)

16. 2006 Qu: 3 (A standard)

17. Bouncing ball
When a ball is bouncing it is constantly changing direction.
As it moves upwards it has a high initial velocity that slows down to 0 at its maximum height.
As it travels downwards it starts at 0 but accelerates due to gravity (increasing its velocity) until it hits the ground and changes direction again.
A v-t graph for a bouncing ball will show motion both above and below the horizontal axis to show the constant change in direction.

18. Bouncing ball simulation

19. Example Draw a v-t graph for the following scenario:
A girl fires a ball vertically into the air from the ground. The ball reaches its maximum height, falls, bounces and then rises to a new, lower, maximum height.

20. Example

21. Example

22. Example

23. Directions of travel In our example we used the following:
below the horizontal axis as travelling upwards
Above the horizontal axis as travelling downwards
Be aware that questions may also use the opposite of the above.
The key thing to remember here is that when the graph crosses the horizontal axis this means the object has changed direction ie changing from up to down.

24. 2000 Qu: 3

25. 2002 Qu: 2

26. Questions
Activity sheets:
Page
You should now be able to answer all questions in class jotter