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What we will do today:

Learn how to revise and describe graphs of motion, including velocity-time and acceleration-time graphs, and how to draw and interpret them. Practice drawing v-t graphs for constant velocity, acceleration, and deceleration scenarios. Understand the relationship between velocity, acceleration, and displacement. This lesson also covers the motion of a bouncing ball and how to create a v-t graph for this scenario.

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What we will do today:

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  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 Acceleration a v s t t t 0 0 0

  6. Graphs Showing Constant Velocity a v s t t t 0 0 0

  7. Graphs Showing Constant Deceleration a v s t 0 t t 0 0

  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)

  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 10 - 20 • You should now be able to answer all questions in class jotter

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