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Chap 02 Solutions copy

Chap 02 Solutions copy - MOTION IN ONE DIMENSION 2 Q2.1...

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2-1 M OTION IN O NE D IMENSION 2 Q2.1. Reason: The elevator must speed up from rest to cruising velocity. In the middle will be a period of constant velocity, and at the end a period of slowing to a rest. The graph must match this description. The value of the velocity is zero at the beginning, then it increases, then, during the time interval when the velocity is constant, the graph will be a horizontal line. Near the end the graph will decrease and end at zero. Assess: After drawing velocity-versus-time graphs (as well as others), stop and think if it matches the physical situation, especially by checking end points, maximum values, places where the slope is zero, etc. This one passes those tests. Q2.2. Reason: (a) The sign conventions for velocity are in Figure 2.7. The sign conventions for acceleration are in Figure 2.26. Positive velocity in vertical motion means an object is moving upward. Negative acceleration means the acceleration of the object is downward. Therefore the upward velocity of the object is decreasing. An example would be a ball thrown upward, before it starts to fall back down. Since it’s moving upward, its velocity is positive. Since gravity is acting on it and the acceleration due to gravity is always downward, its acceleration is negative. (b) To have a negative vertical velocity means that an object is moving downward. The acceleration due to gravity is always downward, so it is always negative. An example of a motion where both velocity and acceleration are negative would be a ball dropped from a height during its downward motion . Since the acceleration is in the same direction as the velocity, the velocity is increasing. Assess: For vertical displacement, the convention is that upward is positive and downward is negative for both velocity and acceleration. Q2.3. Reason: Call “up” the positive direction (this choice is arbitrary, and you could do it the other way, but this is typically easier in cases like this). Also assume that there is no air resistance. This assumption is probably not true (unless the rock is thrown on the moon), but air resistance is a complication that will be addressed later, and for small heavy items like rocks no air resistance is a pretty good assumption if the rock isn’t going too fast. To be able to draw this graph without help demonstrates a good level of understanding of these concepts. The velocity graph will not go up and down as the rock does—that would be a graph of the position. Think carefully about the velocity of the rock at various points during the flight.
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2-2 Chapter 2 At the instant the rock leaves the hand it has a large positive (up) velocity, so the value on the graph at t =0 needs to be a large positive number. The velocity decreases as the rock rises, but the velocity arrow would still point up. So the graph is still above the t axis, but decreasing. At the tippy-top the velocity is zero; that corresponds to a point on the graph where it crosses the t axis. Then as the rock descends with increasing velocity (in the
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Chap 02 Solutions copy - MOTION IN ONE DIMENSION 2 Q2.1...

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