SM_PDF_chapter2

# SM_PDF_chapter2 - Motion in One Dimension CHAPTER OUTLINE...

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23 Motion in One Dimension CHAPTER OUTLINE 2.1 Average Velocity 2.2 Instantaneous Velocity 2.3 Analysis Models The Particle Under Constant Velocity 2.4 Acceleration 2.5 Motion Diagrams 2.6 The Particle Under Constant Acceleration 2.7 Freely Falling Objects 2.8 Context Connection Acceleration Required by Consumers ANSWERS TO QUESTIONS Q2.1 If I count 5.0 s between lightning and thunder, the sound has traveled 331 5 0 1 7 m s s km b ga f . . = . The transit time for the light is smaller by 3 00 10 331 9 06 10 8 5 . . × = × m s m s times, so it is negligible in comparison. Q2.2 Yes. Yes, if the particle winds up in the + x region at the end. Q2.3 Zero. Q2.4 Yes. Yes. Q2.5 No. Consider a sprinter running a straight-line race. His average velocity would simply be the length of the race divided by the time it took for him to complete the race. If he stops along the way to tie his shoe, then his instantaneous velocity at that point would be zero. Q2.6 We assume the object moves along a straight line. If its average velocity is zero, then the displacement must be zero over the time interval, according to Equation 2.2. The object might be stationary throughout the interval. If it is moving to the right at first, it must later move to the left to return to its starting point. Its velocity must be zero as it turns around. The graph of the motion shown to the right represents such motion, as the initial and final positions are the same. In an x vs. t graph, the instantaneous velocity at any time t is the slope of the curve at that point. At t 0 in the graph, the slope of the curve is zero, and thus the instantaneous velocity at that time is also zero. x t t 0 FIG. Q2.6 Q2.7 Yes. If the velocity of the particle is nonzero, the particle is in motion. If the acceleration is zero, the velocity of the particle is unchanging, or is a constant.

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24 Motion in One Dimension Q2.8 Yes. If you drop a doughnut from rest v = 0 a f , then its acceleration is not zero. A common misconception is that immediately after the doughnut is released, both the velocity and acceleration are zero. If the acceleration were zero, then the velocity would not change, leaving the doughnut floating at rest in mid-air. Q2.9 No: Car A might have greater acceleration than B, but they might both have zero acceleration, or otherwise equal accelerations; or the driver of B might have tramped hard on the gas pedal in the recent past. Q2.10 Yes. Consider throwing a ball straight up. As the ball goes up, its velocity is upward v > 0 a f , and its acceleration is directed down a < 0 a f . A graph of v vs. t for this situation would look like the figure to the right. The acceleration is the slope of a v vs. t graph, and is always negative in this case, even when the velocity is positive. v t v 0 FIG. Q2.10 Q2.11 (a) Speeding up as it moves east (b) Braking East (c) Cruising East (d) Braking West (e) Speeding up as it moves west (f) Cruising West (g) Stopped but starting to move East (h) Stopped but starting to move West Q2.12 No. Constant acceleration only. Yes. Zero is a constant.
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