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Graphing Displacement and Velocity Given the position-time graph at right, When is the object travelling forward? When is the object travelling forward? A. 0 – 25 sB. 10 – 25 sC. 10 – 30 s When is the object travelling backward? When is the object travelling backward? A. 30 – 45 sB. 30 – 60 sC. 45 – 60 s When is the object travelling at the greatest speed? When is the object travelling at the greatest speed? A. 10 – 25 sB. 25 – 30 sC. 30 – 45 s

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Graphing Displacement and Velocity Given the position-time graph at right, When is the object travelling forward? When is the object travelling forward? A. 0 – 25 sB. 10 – 25 sC. 10 – 30 s When is the object travelling backward? When is the object travelling backward? A. 30 – 45 sB. 30 – 60 sC. 45 – 60 s When is the object travelling at the greatest speed? When is the object travelling at the greatest speed? A. 10 – 25 sB. 25 – 30 sC. 30 – 45 s

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Graphing Displacement and Velocity Given the position-time graph at right, When is the object travelling forward? When is the object travelling forward? A. 0 – 25 sB. 10 – 25 sC. 10 – 30 s When is the object travelling backward? When is the object travelling backward? A. 30 – 45 sB. 30 – 60 sC. 45 – 60 s When is the object travelling at the greatest speed? When is the object travelling at the greatest speed? A. 10 – 25 sB. 25 – 30 sC. 30 – 45 s

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Graphing Displacement and Velocity Given the position-time graph at right, When is the object travelling forward? When is the object travelling forward? A. 0 – 25 sB. 10 – 25 sC. 10 – 30 s When is the object travelling backward? When is the object travelling backward? A. 30 – 45 sB. 30 – 60 sC. 45 – 60 s When is the object travelling at the greatest speed? When is the object travelling at the greatest speed? A. 10 – 25 sB. 25 – 30 sC. 30 – 45 s

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Relative Velocity SPH3U

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Relative Velocity: Learning Goals The student will be able to perform algebraic operations with vector quantities to solve problems relating to linear motion. (B2.7) The student will be able to perform algebraic operations with vector quantities to solve problems relating to linear motion. (B2.7)

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Relative Velocity: Learning Goals The student will be able to perform algebraic operations with vector quantities to solve problems relating to linear motion. (B2.7) The student will be able to perform algebraic operations with vector quantities to solve problems relating to linear motion. (B2.7) The fundamental super-important physics concept introduced here is inertial frames of reference.

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Velocity Vectors You can add or subtract velocity vectors.

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Velocity Vectors You can add or subtract velocity vectors. e.g. An airplane flying at 80 m/s [N] relative to the air encounters a 10 m/s [N] tailwind. What is the airplane’s velocity relative to the ground?

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Adding Velocity Vectors You can add or subtract velocity vectors. e.g. An airplane flying at 80 m/s [N] relative to the air encounters a 10 m/s [N] tailwind. What is the airplane’s velocity relative to the ground? 80 m/s

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Adding Velocity Vectors You can add or subtract velocity vectors. e.g. An airplane flying at 80 m/s [N] relative to the air encounters a 10 m/s [N] tailwind. What is the airplane’s velocity relative to the ground? 80 m/s10 m/s

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Adding Velocity Vectors You can add or subtract velocity vectors. e.g. An airplane flying at 80 m/s [N] relative to the air encounters a 10 m/s [N] tailwind. What is the airplane’s velocity relative to the ground? The velocity relative to the ground is 90 m/s [N]. 80 m/s 90 m/s 10 m/s

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Adding Velocity Vectors Let’s represent these vectors algebraically: 80 m/s 90 m/s 10 m/s

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Adding Velocity Vectors Let’s represent these vectors algebraically: 80 m/s 90 m/s 10 m/s

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Frames of Reference It is relevant to give the velocity of the airplane relative to both the air and the ground, and we can do so because both the air and the ground are inertial frames of reference. An inertial frame of reference is any object or place that is travelling at a constant velocity (and that velocity may be zero).

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Relative Velocity Example 1 A rides a scooter at 4 m/s [N] past B, who is standing still.

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Relative Velocity Example 1 A rides a scooter at 4 m/s [N] past B, who is standing still. A’s velocity relative to B is 4 m/s [N],

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Relative Velocity Example 1 A rides a scooter at 4 m/s [N] past B, who is standing still. A’s velocity relative to B is 4 m/s [N], and B’s velocity relative to A is 4 m/s [S].

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Relative Velocity Example 1b C rides a scooter at 1 m/s [S] past B, who is standing still. C’s velocity relative to B is ________, and B’s velocity relative to C is ________.

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Relative Velocity Example 1b C rides a scooter at 1 m/s [S] past B, who is standing still. C’s velocity relative to B is 1 m/s [S], and B’s velocity relative to C is 1 m/s [N].

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Relative Velocity Example 2 Or, A rides a scooter at 4 m/s [N] toward C, who is moving at 1 m/s [S]. A’s velocity relative to C is ________. C’s velocity relative to A is ________.

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Relative Velocity Example 2 Or, A rides a scooter at 4 m/s [N] toward C, moving at 1 m/s [S]. A’s velocity relative to C is ________.

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Relative Velocity Example 2 Or, A rides a scooter at 4 m/s [N] toward C, who is moving at 1 m/s [S]. A’s velocity relative to C is 5 m/s [N]. C’s velocity relative to A is ________.

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Relative Velocity Example 2 Or, A rides a scooter at 4 m/s [N] toward C, who is moving at 1 m/s [S]. A’s velocity relative to C is 5 m/s [N]. C’s velocity relative to A is 5 m/s [S].

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Relative Velocity Example 3 Or, A rides a scooter a 4 m/s [N] toward D, moving at 1 m/s [N]. A’s velocity relative to D is ________. D’s velocity relative to A is ________.

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Relative Velocity Example 3 Or, A rides a scooter a 4 m/s [N] toward D, moving at 1 m/s [N]. A’s velocity relative to D is ________.

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Relative Velocity Or, A rides a scooter a 4 m/s [N] toward D, moving at 1 m/s [N]. A’s velocity relative to D is 3 m/s [N]. D’s velocity relative to A is 3 m/s [S].

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A Multi-Object Question A banana boat is travelling at 6 m/s [N] relative to a river flowing at 2 m/s [S]. A monkey on the boat is moving at 2 m/s [N] and throwing a banana behind him at 3 m/s. A bird is flying over the boat at a velocity of 1 m/s [S]. Ms. Rosebery is the observer standing on the river bank watching everything. What is the velocity of the...

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A Multi-Object Question What is the velocity of the...... boat relative to the observer?... monkey relative to the observer?... banana relative to the observer?

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A Multi-Object Question What is the velocity of the...... boat relative to the observer?... monkey relative to the observer?... banana relative to the observer?

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A Multi-Object Question What is the velocity of the...... boat relative to the observer?... monkey relative to the observer?... banana relative to the observer?

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A Multi-Object Question What is the velocity of the...... boat relative to the observer?... monkey relative to the observer?... banana relative to the observer?

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A Multi-Object Question What is the velocity of the...... observer relative to the monkey?... bird relative to the monkey?... banana relative to the bird?

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A Multi-Object Question What is the velocity of the...... observer relative to the monkey?... bird relative to the monkey?... banana relative to the bird?

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A Multi-Object Question What is the velocity of the...... observer relative to the monkey?... bird relative to the monkey?... banana relative to the bird?

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A Multi-Object Question What is the velocity of the...... observer relative to the monkey?... bird relative to the monkey?... banana relative to the bird?

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Why Relative Velocity is Useful Relative velocity is useful when solving problems such as: “Football player A is running at a velocity of 4.0 m/s [N] toward football player B, who is running at a velocity of 3.0 m/s [S]. If they start from a position 25 m apart, how long is it before they collide?”

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Why Relative Velocity is Useful “Football player A is running at a velocity of 4.0 m/s [N] toward football player B, who is running at a velocity of 3.0 m/s [S]. If they start from a position 25 m apart, how long is it before they collide?” Rather than considering 2 objects, we can consider the equivalent situation of B standing still and A running at 7.0 m/s [N] and travelling a distance of 25 m.

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More Practice Homework: Vectors: Relative Velocity

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THEOREM 1 Net Change as the Integral of a Rate The net change in s (t) over an interval [t 1, t 2 ] is given by the integral.

THEOREM 1 Net Change as the Integral of a Rate The net change in s (t) over an interval [t 1, t 2 ] is given by the integral.

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