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PHY 201
Your 'cq_1_04.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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SEED QUESTION 4.0(1_04.1)
The problem:
A ball is moving at 10 cm/s when clock time is 4 seconds, and at 40 cm/s when clock time is 9 seconds.
• Sketch a v vs. t graph and represent these two events by the points (4 sec, 10 cm/s) and (9 s, 40 cm/s).
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
I sketched a graph with (v) as the y-axis (rise) (10 cm/s & 40 cm/s) and (t) as the x-axis (run) (4 sec & 9 sec).
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• Sketch a straight line segment between these points.
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
I sketched the line segment between the two points.
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• What are the rise, run and slope of this segment?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
Sketch a v vs. t graph and represent these two events by the points (4 sec, 10 cm/s) and (9 s, 40 cm/s).
The rise of the segment is (9 sec - 4 sec) / 2 = 5 sec / 2 = 2.5 sec.
The run of the segment is (40 cm/s - 10 cm/s) / 2 = 30 cm/s / 2 = 15 cm/s
The slope of the segment is:
The slope = rise/run
Slope = 15 cm/s / 2.5 sec
@& The rise isn't half the vertical change between the points, it's the whole vertical change.
Similarly the run is the whole horizontal change.
However if you divide half the rise by half the run, you do get the same result as if you divided the entire rise by the entire run.*@
Slope = 6 cm
@& (cm/s) / s is not cm, and the unit of the slope of a v vs. t graph is not the unit of distance.
(cm / s) / s = (cm/s) * (1/s) = cm/s^2, or cm/s/s.
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• What is the area of the graph beneath this segment?
answer/question/discussion: ->->->->->->->->->->->-> (start in the next line):
*The area of a region beneath the graph represents the change in velocity.
The change in velocity is 15 cm/s.
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@& Velocity is the vertical coordinate, so change in velocity is the change in the vertical coordinate.
The area has a very different meaning.
The region beneath the graph is a trapezoid.
How do you find the area of a trapezoid? What two quantities do you multiply?
What is the meaning of each of these quantities in the context of a v vs. t graph?
What would it mean to multiply two quantities with these meaning?
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*#&!*#&!
@& Please submit a revision. You might well reason all of this out, since you've got a really good start on it. But you might also have some additional questions, which I'll be glad to answer.
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