The document provides an overview of key concepts relating to mapping space and time, including maps and vectors, distance-time graphs, speed and velocity, Pythagoras' theorem, and velocity-time graphs. It defines vectors as having magnitude and direction, and explains how to calculate resultant vectors. It also discusses using graphs to determine instantaneous and average speed/velocity, and how distance traveled relates to the area under graphs. Worked examples are provided for practice questions.

9. 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

14. 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?

15. Plot a Distance Time Graph for 1 marble journey…

16. Distance Time Graph Time (s) Distance (m) Gradient = Distance /Time = Speed Or dy / dx But it is different at different places?

17. 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

18. 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

19. Try this What is the instantaneous speed here

20. Try this

21. Try this What is the average speed between 40 and 60 mins?

22. Try this

26. Write these into your book with answers… For each of the graphs in question 2, calculate the distance travelled overall.

27. To recap on last lesson, answer these in the back of your book… Distance travelled is area under graph…

28. Making a Velocity Time Graph…