Chap 02 SM - Chapter 2 Motion in One Dimension Conceptual...

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55 Chapter 2 Motion in One Dimension Conceptual Problems 1 What is the average velocity over the round trip of an object that is launched straight up from the ground and falls straight back down to the ground? 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 Δ Δ = 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 Δ 0 Δ Δ av = = = t t y v 2 An object thrown straight up falls back and is caught at the same place it is launched from. Its time of flight is T , its maximum height is H . Neglect air resistance. The correct expression for its average speed for the entire flight is ( a ) H / T , ( b ) 0, ( c ) H /(2 T ), and ( d ) 2 H / T . 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 elapsed time, in this case 2 H / T . ) ( d is correct. Remarks : Because this motion involves a round trip, if the question asked for "average velocity," the answer would be zero. 3 Using the information in the previous question, what is its average speed just for the first half of the trip? What is its average velocity for the second half of the trip? (Answer in terms of H and T .) Determine the Concept Under all circumstances, including constant acceleration , the definition of the average speed is the ratio of the total distance traveled to the elapsed time. The average velocity, on the other hand, is the ratio of the displacement to the elapsed time.
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Chapter 2 56 The average speed for the first half of the trip is the height to which the object rises divided by one-half its time of flight: T H T H v 2 2 1 half 1st av, = = The average velocity for the second half of the trip is the distance the object falls divided by one-half its time of flight: T H T H 2 vel 2 1 half 2nd av, = = Remarks: We could also say that the average velocity for the second half of the trip is 2 H / T. 4 Give an everyday example of one-dimensional motion where ( a ) the velocity is westward and the acceleration is eastward, and ( b ) the velocity is northward and the acceleration is northward. 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 ) An example of one-dimensional motion where the velocity is westward and acceleration is eastward is a car traveling westward and slowing down.
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This note was uploaded on 02/28/2012 for the course PHYSICS 122 taught by Professor Goussiou during the Spring '12 term at University of Washington.

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Chap 02 SM - Chapter 2 Motion in One Dimension Conceptual...

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