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Vectors A runner ran 400 m around a track. What was her displacement? A runner ran 400 m around a track. What was her displacement? A. zeroB. 400 mC. 400 m [around] A tiger paces 20 m [W] and 10 m [E]. What was the tiger’s displacement? A tiger paces 20 m [W] and 10 m [E]. What was the tiger’s displacement? A. zeroB. 30 mC. 10 m [E]D. 10 m [W] True or false?: The average velocity of an object can be zero even if the object is moving. True or false?: The average velocity of an object can be zero even if the object is moving.

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Vectors A runner ran 400 m around a track. What was her displacement? A runner ran 400 m around a track. What was her displacement? A. zeroB. 400 mC. 400 m [around] A tiger paces 20 m [W] and 10 m [E]. What was the tiger’s displacement? A tiger paces 20 m [W] and 10 m [E]. What was the tiger’s displacement? A. zeroB. 30 mC. 10 m [E]D. 10 m [W] True or false?: The average velocity of an object can be zero even if the object is moving. True or false?: The average velocity of an object can be zero even if the object is moving.

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Vectors A runner ran 400 m around a track. What was her displacement? A runner ran 400 m around a track. What was her displacement? A. zeroB. 400 mC. 400 m [around] A tiger paces 20 m [W] and 10 m [E]. What was the tiger’s displacement? A tiger paces 20 m [W] and 10 m [E]. What was the tiger’s displacement? A. zeroB. 30 mC. 10 m [E]D. 10 m [W] True or false?: The average velocity of an object can be zero even if the object is moving. True or false?: The average velocity of an object can be zero even if the object is moving.

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Vectors A runner ran 400 m around a track. What was her displacement? A runner ran 400 m around a track. What was her displacement? A. zeroB. 400 mC. 400 m [around] A tiger paces 20 m [W] and 10 m [E]. What was the tiger’s displacement? A tiger paces 20 m [W] and 10 m [E]. What was the tiger’s displacement? A. zeroB. 30 mC. 10 m [E]D. 10 m [W] True or false?: The average velocity of an object can be zero even if the object is moving. True or false?: The average velocity of an object can be zero even if the object is moving.

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Graphing Displacement and Velocity: Learning Goal The student will be able to create and analyse displacement-time graphs and velocity-time graphs of motion in one dimension (using slopes of displacement-time graphs to find velocities and using the area under velocity-time graphs to find displacement). (B2.2) The student will be able to create and analyse displacement-time graphs and velocity-time graphs of motion in one dimension (using slopes of displacement-time graphs to find velocities and using the area under velocity-time graphs to find displacement). (B2.2)

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Graphing Displacement and Velocity SPH3U

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Practice Question 1 Redux Although Leah jogged at a constant speed for 1 minute, she spent the first 30 s of that minute jogging North and the second 30 s jogging South.

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Practice Question 1 Redux Her velocity, which is a vector quantity defined as the rate of change in her displacement, was therefore 3 m/s [North] (or 3 m/s if we designate North the positive direction) for the first 30 s and 3 m/s [South] (or -3 m/s if we designate South the negative direction) for the second 30 s. + _

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Practice Question 1 Redux Plot Leah's velocity on the grid below with time on the horizontal axis and velocity on the vertical axis. Label your axes! (Note that there is a discontinuity at 30 s.)

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Practice Question 1 Redux Plot Leah's velocity on the grid below with time on the horizontal axis and velocity on the vertical axis. Label your axes! (Note that there is a discontinuity at 30 s.)

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Practice Question 1 Redux Plot Leah's velocity on the grid below with time on the horizontal axis and velocity on the vertical axis. Label your axes! (Note that there is a discontinuity at 30 s.)

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Area Under The area under a velocity-time graph will be equal to the displacement. Use the graph to calculate the displacement at 0 s, 10 s, 20 s, etc. Note that an area under the horizontal axis will be a negative area.

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Area Under Example: At 40 seconds, the area under the graph is:

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Displacement-Time Plot the data points in the table with time on the horizontal axis and displacement on the vertical axis. Label your axes!

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Displacement-Time

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Displacement-Time Where is Leah relative to her starting position at the end of the 1 minute?

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Displacement-Time At her starting point.

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Average Velocity We can find the average velocity over any time interval by finding the slope of the line connecting the endpoints of the interval on the displacement-time graph. What was Leah’s average velocity over the 1 minute time interval?

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Average Velocity We can find the average velocity over any time interval by finding the slope of the line connecting the endpoints of the interval on the displacement-time graph. What was Leah’s average velocity over the 1 minute time interval? 0 m/s because her displacement was zero.

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More Practice Interpreting Graphs The graph at right shows the position-time or displacement-time graph of a radio controlled car. (Positive = [forward]) On a separate sheet of graph paper, Describe each segment of the motion in words. Describe each segment of the motion in words. Sketch the corresponding distance-time graph. Sketch the corresponding distance-time graph. Sketch the corresponding velocity-time graph. Sketch the corresponding velocity-time graph.

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More Practice Interpreting Graphs Describe each segment of the motion in words. Describe each segment of the motion in words. Between 0 and 2 s, the car is travelling at

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More Practice Interpreting Graphs Describe each segment of the motion in words. Describe each segment of the motion in words. Between 0 and 2 s, the car is travelling at 4 m/s [fwd]. Between 2 s and 4 s,

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More Practice Interpreting Graphs Describe each segment of the motion in words. Describe each segment of the motion in words. Between 0 and 2 s, the car is travelling at 4 m/s [fwd]. Between 2 s and 4 s, the car is at rest. Between 4 s and 9 s,

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More Practice Interpreting Graphs Describe each segment of the motion in words. Describe each segment of the motion in words. Between 0 and 2 s, the car is travelling at 4 m/s [fwd]. Between 2 s and 4 s, the car is at rest. Between 4 s and 9 s, the car is travelling at 2 m/s [back]. Between 9 s and 10 s,

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More Practice Interpreting Graphs Describe each segment of the motion in words. Describe each segment of the motion in words. Between 0 and 2 s, the car is travelling at 4 m/s [fwd]. Between 2 s and 4 s, the car is at rest. Between 4 s and 9 s, the car is travelling at 2 m/s [back]. Between 9 s and 10 s, the car is at rest.

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More Practice Interpreting Graphs On a separate sheet of graph paper, Sketch the corresponding distance-time graph. Sketch the corresponding distance-time graph.

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More Practice Interpreting Graphs On a separate sheet of graph paper, Sketch the corresponding distance-time graph. Sketch the corresponding distance-time graph.

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More Practice Interpreting Graphs On a separate sheet of graph paper, Sketch the corresponding velocity-time graph. Sketch the corresponding velocity-time graph.

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More Practice Interpreting Graphs On a separate sheet of graph paper, Sketch the corresponding velocity-time graph. Sketch the corresponding velocity-time graph.

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