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**Motion in One Dimension**

Chapter 2 Motion in One Dimension

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Quick Quiz 2.1 Under which of the following conditions is the magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval? (a) A particle moves in the + x direction without reversing. (b) A particle moves in the - x direction without reversing. (c) A particle moves in the + x direction and then reverses the direction of its motion. (d) There are no conditions for which this is true.

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Quick Quiz 2.1 Answer: (c). If the particle moves along a line without changing direction, the displacement and distance traveled over any time interval will be the same. As a result, the magnitude of the average velocity and the average speed will be the same. If the particle reverses direction, however, the displacement will be less than the distance traveled. In turn, the magnitude of the average velocity will be smaller than the average speed.

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Quick Quiz 2.2 If a car is traveling eastward and slowing down, what is the direction of the force on the car that causes it to slow down? (a) eastward (b) westward (c) neither of these

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Quick Quiz 2.2 Answer: (b). If the car is slowing down, a force must be pulling in the direction opposite to its velocity.

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**Position of the Car at Various Times**

Quick Quiz 2.3 Make a velocity–time graph for the car in the figure below. The speed limit posted on the road sign is 30 km/h. True or false: The car exceeds the speed limit at some time within the interval. Position of the Car at Various Times at t (s) x (m) A 30 B 10 52 C 20 38 D E 40 -37 F 50 -53

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Quick Quiz 2.3 Answer: False. Your graph should look something like the following. This vx-t graph shows that the maximum speed is about 5.0 m/s, which is 18 km/h ( = 11 mi/h), and so the driver was not speeding.

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**Quick Quiz 2.4 Which of the following is true?**

(a) If a car is traveling eastward, its acceleration is eastward. (b) If a car is slowing down, its acceleration must be negative. (c) A particle with constant acceleration can never stop and stay stopped.

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Quick Quiz 2.4 Answer: (c) If a particle with constant acceleration stops and its acceleration remains constant, it must begin to move again in the opposite direction. If it did not, the acceleration would change from its original constant value to zero. Choice (a) is not correct because the direction of acceleration is not specified by the direction of the velocity. Choice (b) is also not correct by counterexample – a car moving in the –x direction and slowing down has a positive acceleration.

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Quick Quiz 2.5 In Figure 2.11, match each vx-t graph on the left with the ax-t graph on the right that best describes the motion.

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**Quick Quiz 2.5 Answer: a -> e; b -> d, c -> f**

Graph (a) has a constant slope, indicating a constant acceleration; this is represented by graph (e). Graph (b) represents a speed that is increasing constantly but not at a uniform rate. Thus, the acceleration must be increasing, and the graph that best indicates this is (d). Graph (c) depicts a velocity that first increases at a constant rate, indicating constant acceleration. Then the velocity stops increasing and becomes constant, indicating zero acceleration. The best match to this situation is graph (f).

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Quick Quiz 2.6 A ball is thrown upward. While the ball is in free fall, its acceleration (a) increases (b) decreases (c) increases and then decreases (d) decreases and then increases (e) remains constant

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Quick Quiz 2.6 Answer: (e). For the entire time interval that the ball is in free fall, the acceleration is that due to gravity.

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Quick Quiz 2.7 After a ball is thrown upward and is in the air, its speed (a) increases (b) decreases (c) increases and then decreases (d) decreases and then increases (e) remains the same

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Quick Quiz 2.7 Answer: (d). While the ball is rising, it is slowing down. After reaching the highest point, the ball begins to fall and its speed increases.

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Quick Quiz 2.8 Which values represent the ball’s vertical velocity and acceleration at points A, C, and E in the figure below? (a) vy = 0, ay = m/s2 (b) vy = 0, ay = 9.80 m/s2 (c) vy = 0, ay = 0 (d) vy = m/s, ay = 0

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Quick Quiz 2.8 Answer: (a). At the highest point, the ball is momentarily at rest, but still accelerating at –g.

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