course Phy 121
13/Jul/2010 21:19
The problem: A graph is constructed representing velocity vs. clock time for the interval between clock times t = 5 seconds and t = 13 seconds. The graph consists of a straight line from the point (5 sec, 16 cm/s) to the point (13 sec, 40 cm/s).
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What is the clock time at the midpoint of this interval?
answer/question/discussion (start in the next line):
Change in clock time = 13 sec - 5 sec = 4 sec
Midpoint = 5 sec + 4 sec = 9 sec
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What is the velocity at the midpoint of this interval?
answer/question/discussion (start in the next line):
Total change in clock time = 8 sec
Total change in velocity = 40 cm/sec - 16 cm / sec = 24 cm/sec
Average change in velocity = 24 cm/sec / 8 sec = 3 (cm/sec)/sec
Velocity at midpoint = 16 cm/s (Initial velocity) + (3 (cm/sec)/sec * 4 sec) = 28 cm/sec
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How far do you think the object travels during this interval?
answer/question/discussion (start in the next line):
Velocity Change - Initial to Midpoint = 28 cm/sec - 16 cm-sec = 12 cm/sec
Average Velocity - Initial to Midpoint = 16 cm/sec + (12 (cm/sec)/ 2) = 22 cm/sec
Displacement = 22 cm/sec * 4 sec = 88 cm
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By how much does the clock time change during this interval?
answer/question/discussion (start in the next line):
Change in clock = 9 sec - 5 sec = 4 sec
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By how much does velocity change during this interval?
answer/question/discussion (start in the next line):
Velocity Change - Initial to Midpoint = 28 cm/sec - 16 cm-sec = 12 cm/sec
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What is the average rate of change of velocity with respect to clock time on this interval?
answer/question/discussion (start in the next line):
Average Velocity - Initial to Midpoint = 16 cm/sec + (12 (cm/sec)/ 2) = 22 cm/sec
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What is the rise of the graph between these points?
answer/question/discussion (start in the next line):
x = velocity, y = elapsed time: Rise = 24
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What is the run of the graph between these points?
answer/question/discussion (start in the next line):
x = velocity, y = elapsed time: Run = 8
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What is the slope of the graph between these points?
answer/question/discussion (start in the next line):
x = velocity, y = elapsed time: Slope = 3
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What does the slope of the graph tell you about the motion of the object during this interval?
answer/question/discussion (start in the next line):
Motion is increasing left to right - positive slope
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What is the average rate of change of the object's velocity with respect to clock time during this interval?
answer/question/discussion (start in the next line):
Average change in velocity = 24 cm/sec / 8 sec = 3 (cm/sec)/sec
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Copy and paste your work into the box below and submit as indicated:
Your instructor is trying to gauge the typical time spent by students on these questions. Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
* Approximately how much time did you spend on this question?
20 min"
You did a lot of your calculations for initial to midpoint of the interval, and you did specify this. For the subinterval from initial to midpoint your results are correct.
However the requested solutions were for the entire interval.
Check the link. I doubt very much that you'll have any questions; you will almost certainly understand everything you see there.
&#See any notes I might have inserted into your document. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
&#No revision is necessary unless you have a question, or something you want me to review. &#