Phy 121
Your 'cq_1_02.2' 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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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).
What is the clock time at the midpoint of this interval?
answer/question/discussion: 9 sec - you arrive at this number by adding 5+13 and then dividing by 2
What is the velocity at the midpoint of this interval?
answer/question/discussion:1.85 cm/sec^2 - you arrive at this number by first finding the displacement of 16cm/s and 40cm/s and then dividing by time elapsed which was 13 sec.
16 cm/s and 40 cm/s are not positions in the difference between these quantities is not displacement.
These two quantities are velocities, so the difference will be the change in velocity.
However you are asked for the velocity at the midpoint of the interval. After identifying the two given quantities as the velocities at the beginning and the end of the interval, how do you then find the velocity at the midpoint?
How far do you think the object travels during this interval?
answer/question/discussion:24 cm/s - I arrived at this number by subtacting 16 from 40
This would give you the change in velocity, not the distance the object travels.
By how much does the clock time change during this interval?
answer/question/discussion:8 seconds - I arrived at this number by subtacting 5 from 13
By how much does velocity change during this interval?
answer/question/discussion:-4cm/s is the velocity change
You don't say how you got this, and it isn't clear how you arrived at this result, but it is not correct. See my notes above and see if he can find the change in the velocity.
What is the average rate of change of velocity with respect to clock time on this interval?
answer/question/discussion: I can’t come up with an answer.
What is the definition of the average rate of change of velocity of respect to clock time?
What is the change in velocity?
What is the change in clock time?
What therefore is the requested average rate?
What is the rise of the graph between these points?
answer/question/discussion: I think it would be at the highest point which is (13 sec, 40cm/s)
The rise between two points on a graph is the difference in the 'vertical' coordinates of those points. What are the 'vertical' coordinates of the two points, and what is the difference between the first and second 'vertical' coordinate?
What is the run of the graph between these points?
The run is the difference between the first and second 'horizontal' coordinate.
answer/question/discussion: I think that the run would be how far it traveled from the first point to the last so the answer would be (8sec, 24 cm/s)
Actually 8 sec turns out to be the run and 24 cm/s turns out to be the rise. Do you see why this is so?
What is the slope of the graph between these points?
answer/question/discussion: I think the slope is 2.67. I arrived at this answer by using the equation P=mQ+b where I used 15 for P and 40 for Q and 0 for b since I did not know what vertical intercept was
This is not a bad attempt, but it isn't correct. See my above notes -- it's actually simpler than what you did.
What does the slope of the graph tell you about the motion of the object during this interval? answer/question/discussion: That it is moving in a slowly upward motion.
What is the average rate of change of the object's velocity with respect to clock time during this interval?
answer/question/discussion:-4 cm/s and I arrived at this number by subtracting 40 cm/s from 16 cm/s and then dividing by the difference between 5 sec and 13 seconds which was 8 seconds
You did the right thing here, except that you should have found the difference between 16 cm/s and 40 cm/s, which is positive. However the result of your calculation would be -3 cm/s^2, not -4 cm/s; subtracting in the correct order would yield 3 cm/s^2.
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55 minutes
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I would really like to know if I done these questions right.
You made a very good attempt and had a number of correct steps. However you had some errors also.
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