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Graphical Analysis of Motion Physics 11 Graphing Motion • Graphs are a powerful way of describing the motion of an object. • In motion, the following graphs are often analyzed: – Position-Time – Velocity-Time – Acceleration-Time • This section will study the relationships between these graphs. Position-Time Graph • A position-time graph shows where the object in question is located at any point in time. • A position-time graph will also give you the object's average velocity over a period of time. Slope in a Graph Slope (given symbol m) for a x-y graph equals: 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑦2 − 𝑦1 𝑚= = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 𝑥2 − 𝑥1 In the case of a position-time graph, the slope is : ∆𝑑 𝑚= ∆𝑡 which is the definition of average velocity. Example Draw the velocity-time graph of the object in motion described in the graph below: Negative Velocities and Average Speed • When the velocity of an object changes from positive to negative (or vice versa), it means that it has changed direction. • On a position-time graph, this occurs at the maximums and minimums. Instantaneous Speed on a graph • In reality graphs are rarely straight lines. You then have to analyze curves. • To find the instantaneous speed (or speed at a specific time) on such a graph, you need to calculate the slope of the tangent line on that point. Quick Practice p.57 # 4 Velocity-Time Graph • What do you obtain with the slope of a velocity-time graph? • How can you find the displacement of an object using a velocity-time graph? Example Jonathan can run as shown in the graph below. a) How fast is Jonathan running at: – 1 second? – 4 seconds? – 5 seconds? b) For all 3 sections in the graph, find: – Jonathan’s acceleration – Jonathan’s displacement Match the following graphs with their corresponding description Acceleration-Time Graph • What does it mean when an object like a car accelerates? • Can acceleration increase or decrease? Example • Using the graph below, find for each segment: – The object’s velocity – The object’s displacement • What assumptions do you have to make? Jerk • In physics, a jerk is the rate of change of acceleration. Quick Practice p.70 # 3, 5, 7