12 •• Which of the position-versus-time curves in Figure 2 ...



12 •• Which of the position-versus-time curves in Figure 2-28 best shows the motion of an object (a) with positive acceleration, (b) with constant positive velocity, (c) that is always at rest, and (d) with negative acceleration? (There may be more than one correct answer for each part of the problem.)

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Figure 2-28  Problem 12

13 •• Which of the velocity-versus-time curves in Figure 2-29 best describes the motion of an object (a) with constant positive acceleration, (b) with positive acceleration that is decreasing with time, (c) with positive acceleration that is increasing with time, and (d) with no acceleration? (There may be more than one correct answer for each part of the problem.) 

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Figure 2-29  Problem 13

Answer:

(a) b, (b) c, (c) d, (d) e

14 •• The diagram in Figure 2-30 tracks the location of an object moving in a straight line along the x axis. Assume that the object is at the origin at t = 0. Of the five times shown, which time (or times) represents when the object is (a) farthest from the origin, (b) at rest for an instant, (c) in the midst of being at rest for a while, and (d) moving away from the origin?

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Figure 2-30  Problem 14 and 15

15 •• An object moves along a straight line. Its position-versus-time graph is shown in Figure 2-30. At which time or times is its (a) speed at a minimum, (b) acceleration positive, and (c) velocity negative? 

Answer:

(a) B, D, and E, (b) A and D, (c) C

16 •• For each of the four graphs of x versus t in Figure 2-31 answer the following questions. (a) Is the velocity at time t2 greater than, less than, or equal to the velocity at time t1? (b) Is the speed at time t2 greater than, less than, or equal to the speed at time t1?

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Figure 2-31  Problem 16

23 •• Context-Rich You are driving a Porsche that accelerates uniformly from 80.5 km/h (50 mi/h) at t = 0.00 s to 113 km/h (70 mi/h) at t = 9.00 s. (a) Which graph in Figure 2-32 best describes the velocity of your car? (b) Sketch a position-versus-time graph showing the location of your car during these nine seconds, assuming we let its position x be zero at t = 0.

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Figure 2-32  Problem 23

29 •• The positions of two cars in parallel lanes of a straight stretch of highway are plotted as functions of time in the Figure 2-33. Take positive values of x as being to the right of the origin. Qualitatively answer the following: (a) Are the two cars ever side by side? If so, indicate that time (those times) on the axis. (b) Are they always traveling in the same direction, or are they moving in opposite directions for some of the time? If so, when? (c) Are they ever traveling at the same velocity? If so, when? (d) When are the two cars the farthest apart? (e) Sketch (no numbers) the velocity versus time curve for each car. 

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Figure 2-33  Problem 29

Answer:

(a) Yes, when the graphs intersect, (b) Yes, when the slopes of the curves have opposite signs, (c) Yes, when the curves have the same slope, (d) The two cars are farthest apart at the instant the two curves are farthest apart in the x direction.

30 •• A car driving at constant velocity passes the origin at time t = 0. At that instant, a truck, at rest at the origin, begins to accelerate uniformly from rest. Figure 2-34 shows a qualitative plot of the velocities of truck and car as functions of time. Compare their displacements (from the origin), velocities, and accelerations at the instant that their curves intersect.

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Figure 2-34  Problem 30

Answer:

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32 •• Which graph (or graphs), if any, of vx versus t in Figure 2-36 best describes the motion of a particle with (a) positive velocity and increasing speed, (b) positive velocity and zero acceleration, (c) constant nonzero acceleration, and (d) a speed decrease?

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Figure 2-36  Problem 32

Answer:

(a) d, (b) b, (c) None, (d) c and d

34 •• Sketch a v-versus-t curve for each of the following conditions: (a) Acceleration is zero and constant while velocity is not zero. (b) Acceleration is constant but not zero. (c) Velocity and acceleration are both positive. (d) Velocity and acceleration are both negative. (e) Velocity is positive and acceleration is negative. (f) Velocity is negative and acceleration is positive. (g) Velocity is momentarily zero but the acceleration is not zero.

35 •• Figure 2-37 shows nine graphs of position, velocity, and acceleration for objects in motion along a straight line. Indicate the graphs that meet the following conditions: (a) Velocity is constant, (b) velocity reverses its direction, (c) acceleration is constant, and (d) acceleration is not constant. (e) Which graphs of position, velocity, and acceleration are mutually consistent?

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Figure 2-37  Problem 35

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