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.
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Chapter 8
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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
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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?
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