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Chapter 8 – Mapping Space and Time 8.1 - Journeys We will find out:  that speed is distance over time;  v = s / t ;  that speed can be calculated from the gradient of a distance–time graph;  the meanings of average and instantaneous speeds and how these are calculated from speed–time graphs;  the meaning of the area under a speed–time graph and how to estimate this.
What is Speed?  Velocity? Speed is how far something travels in a certain time… Think about a jet coming into land.. ,[object Object],[object Object],[object Object],Is its speed the same as its velocity???
Speed and Velocity Speed =  Distance Travelled / Time Taken = m/s IT IS A SCALAR QUANTITY – IT ONLY HAS MAGNITUDE Velocity =  Distance Travelled / Time Taken = m/s IT IS A VECTOR – IT HAS MAGNITUDE  AND  DIRECTION Distance Speed x Time
Distance Time Graph ,[object Object],Time (s) Distance (m)
Distance Time Graph ,[object Object],Time (s) Distance (m) A B C D Describe each section, A to D
Distance Time Graph Time (s) Distance (m) Moving at constant speed Stationary Constant speed but faster than A Moving back towards start point What else can we calculate from the graph?
Plot a Distance Time Graph for 1 marble journey…
Distance Time Graph Time (s) Distance (m) Gradient = Distance /Time = Speed Or  dy / dx But it is different at different places?
Instantaneous Speed Time (s) Distance (m) What is the speed here? Calculate the gradient of the TANGENT on your graph The Gradient at this point is the INSTANTANEOUS SPEED
Average Speed Time (s) Distance (m) What is the AVERAGE Speed for the whole journey? Calculate the gradient of the CHORD on your graph The Gradient of the CHORD is the AVERAGE SPEED
Try this What is the instantaneous speed here
Try this
Try this What is the average speed between 40 and 60 mins?
Try this
Using the speed triangle, try these… ,[object Object],[object Object],[object Object]
Using the speed triangle, try these… ,[object Object],[object Object],[object Object],[object Object],[object Object]
Velocity Time Graphs ,[object Object],[object Object]
Velocity Time Graph ,[object Object],Time (s) Velocity (m/s) Speeding up – constant acceleration Constant Velocity Constant Acceleration Slowing Down - decelerating Stationary
Write these into your book with answers… For each of the graphs in question 2, calculate the distance travelled overall.
To recap on last lesson, answer these in the back of your book… Distance travelled is area under graph…
Making a Velocity Time Graph…
Velocity Time Graph ,[object Object],Time (s) Velocity (m/s)
Questions to Try ,[object Object],[object Object],[object Object],[object Object]
 

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Chapter 8

  • 1. Chapter 8 – Mapping Space and Time 8.1 - Journeys We will find out:  that speed is distance over time; v = s / t ;  that speed can be calculated from the gradient of a distance–time graph;  the meanings of average and instantaneous speeds and how these are calculated from speed–time graphs;  the meaning of the area under a speed–time graph and how to estimate this.
  • 2.
  • 3. Speed and Velocity Speed = Distance Travelled / Time Taken = m/s IT IS A SCALAR QUANTITY – IT ONLY HAS MAGNITUDE Velocity = Distance Travelled / Time Taken = m/s IT IS A VECTOR – IT HAS MAGNITUDE AND DIRECTION Distance Speed x Time
  • 4.
  • 5.
  • 6. Distance Time Graph Time (s) Distance (m) Moving at constant speed Stationary Constant speed but faster than A Moving back towards start point What else can we calculate from the graph?
  • 7. Plot a Distance Time Graph for 1 marble journey…
  • 8. Distance Time Graph Time (s) Distance (m) Gradient = Distance /Time = Speed Or dy / dx But it is different at different places?
  • 9. Instantaneous Speed Time (s) Distance (m) What is the speed here? Calculate the gradient of the TANGENT on your graph The Gradient at this point is the INSTANTANEOUS SPEED
  • 10. Average Speed Time (s) Distance (m) What is the AVERAGE Speed for the whole journey? Calculate the gradient of the CHORD on your graph The Gradient of the CHORD is the AVERAGE SPEED
  • 11. Try this What is the instantaneous speed here
  • 13. Try this What is the average speed between 40 and 60 mins?
  • 15.
  • 16.
  • 17.
  • 18.
  • 19. Write these into your book with answers… For each of the graphs in question 2, calculate the distance travelled overall.
  • 20. To recap on last lesson, answer these in the back of your book… Distance travelled is area under graph…
  • 21. Making a Velocity Time Graph…
  • 22.
  • 23.
  • 24.