ism_chapter_02

ism_chapter_02 - Chapter 2 Motion in One Dimension...

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33 Chapter 2 Motion in One Dimension Conceptual Problems 1 Determine the Concept The "average velocity" is being requested as opposed to "average speed". The average velocity is defined as the change in position or displacement divided by the change in time. t y v = av The change in position for any "round trip" is zero by definition. So the average velocity for any round trip must also be zero. 0 0 av = = = t t y v *2 Determine the Concept The important concept here is that "average speed" is being requested as opposed to "average velocity". Under all circumstances, including constant acceleration , the definition of the average speed is the ratio of the total distance traveled ( H + H ) to the total time elapsed, in this case 2 H / T . correct. is ) ( d Remarks : Because this motion involves a round trip, if the question asked for "average velocity," the answer would be zero. 3 Determine the Concept Flying with the wind, the speed of the plane relative to the ground ( v PG ) is the sum of the speed of the wind relative to the ground ( v WG ) and the speed of the plane relative to the air ( v PG = v WG + v PA ). Flying into or against the wind the speed relative to the ground is the difference between the wind speed and the true air speed of the plane ( v g = v w v t ). Because the ground speed landing against the wind is smaller than the ground speed landing with the wind, it is safer to land against the wind. 4 Determine the Concept The important concept here is that a = dv/dt, where a is the acceleration and v is the velocity. Thus, the acceleration is positive if dv is positive; the acceleration is negative if dv is negative. ( a ) Let’s take the direction a car is moving to be the positive direction: Because the car is moving in the direction we’ve chosen to be positive, its velocity is positive ( dx > 0). If the car is braking, then its velocity is decreasing ( dv < 0) and its acceleration ( dv / dt ) is negative. ( b ) Consider a car that is moving to Because the car is moving in the direction
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Chapter 2 34 the right but choose the positive direction to be to the left: opposite to that we’ve chosen to be positive, its velocity is negative ( dx < 0). If the car is braking, then its velocity is increasing ( dv > 0) and its acceleration ( dv / dt ) is positive. *5 Determine the Concept The important concept is that when both the acceleration and the velocity are in the same direction, the speed increases. On the other hand, when the acceleration and the velocity are in opposite directions, the speed decreases. ( a ) . be must nt displaceme your negative, remains ity your veloc Because negative ( b ) reached. is wall the until walking, of speed the slow gradually steps five last the During direction. negative the as your trip of direction the Define ( c ) A graph of v as a function of t that is consistent with the conditions stated in the problem is shown to the right: -5 -4 -3 -2 -1 0 0 0.5 1 1.5 2 2.5 t (s) v (m/s) 6 Determine the Concept True. We can use the definition of average velocity to express the displacement x as x = v av t . Note that, if the acceleration is constant, the average
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ism_chapter_02 - Chapter 2 Motion in One Dimension...

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