Phy 201
Your 'cq_1_01.1' 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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The problem:
Here is the definition of rate of change of one quantity with respect to another:
The average rate of change of A with respect to B on an interval is
• average rate of change of A with respect to B = (change in A) / (change in B)
Apply the above definition of average rate of change of A with respect to B to each of the following. Be sure to identify the quantity A, the quantity B and the requested average rate.
• If the position of a ball rolling along a track changes from 10 cm to 20 cm while the clock time changes from 4 seconds to 9 seconds, what is the average rate of change of its position with respect to clock time during this interval?
answer/question/discussion: (20cm-10cm)/(9s-4s) = (10cm)/(5s) = 2cm/s
• If the velocity of a ball rolling along a track changes from 10 cm / second to 40 cm / second during an interval during which the clock time changes by 3 seconds, then what is the average rate of change of its velocity with respect to clock time during this interval?
answer/question/discussion: (40cm-10cm)/(3s) = (30cm)/(3s) = 10cm/s
None of the quantities involved in this calculation are 40 cm, and none are 10 cm.
The quantities 40 cm/s and 10 cm/s are, however, relevant.
• If the average rate at which position changes with respect to clock time is 5 cm / second, and if the clock time changes by 10 seconds, by how much does the position change?
answer/question/discussion: (5cm)/(10s) = .5cm/s
• You will be expected hereafter to know and apply, in a variety of contexts, the definition given in this question. You need to know this definition word for word. If you try to apply the definition without using all the words it is going to cost you time and it will very likely diminish your performance. Briefly explain how you will ensure that you remember this definition.
answer/question/discussion: Ave rate of change of A with respect to B on an interval is the (change in A)/(change in B)
• You are asked in this exercise to apply the definition, and given a general procedure for doing so. Briefly outline the procedure for applying this definition, and briefly explain how you will remember to apply this procedure.
answer/question/discussion: The procedure involves subtracting to determine the change in both the quantities A and B, then dividing A by B to determine the Avg rate of change.
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15min
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You apply the definition correctly (or nearly so) on two of the three questions, which is good. However there are some errors in the application, and you didn't apply the definition on the third question.
I've noted one of your errors above. You have some additional errors.
The following is a solution to the given problem. Please see the given solution and submit a self-critique of your solution, by copying your solution into a text editor and inserting revisions, questions, and/or self-critiques, marking your insertions with ####.
If the position of a ball rolling along a track changes from 10 cm to 20 cm while the clock time changes from 4 seconds to 9 seconds, what is the average rate of change of its position with respect to clock time during this interval?
We solve this by applying the definition of average rate of change.
10 cm and 20 cm are positions, so quantity A is position and quantity B is change in clock time.
The average rate of change of position with respect to clock time is therefore
ave rate = change in position / change in clock time = 10 cm / (5 s) = 2 cm/s.
The average rate of change of position with respect to clock time is by definition the average velocity.
If the velocity of a ball rolling along a track changes from 10 cm / second to 40 cm / second during an interval during which the clock time changes by 3 seconds, then what is the average rate of change of its velocity with respect to clock time during this interval?
We solve this by applying the definition of average rate of change.
10 cm / sec and 40 cm / sec are velocities, so quantity A is velocity and quantity B is change in clock time.
The average rate of change of velocity with respect to clock time is therefore
ave rate = change in velocity / change in clock time = (30 cm / s) / (3 s) = 10 (cm/s) / (s) = 10 (cm/s) * (1/s) = 10 cm/s^2.
Note that this result is in units of cm/s^2, not cm/s.
The average rate of change of position with respect to clock time is by definition the average acceleration.
If the average rate at which position changes with respect to clock time is 5 cm / second, and if the clock time changes by 10 seconds, by how much does the position change?
The average rate of change of position with respect to clock time is
ave rate = (change in position) / (change in clock time). It follows that
change in position = ave rate * change in clock time, or more specifically
change in position = ave rate of change of position with respect to clock time * change in clock time. Thus
change in position = 5 cm/s * 10 s = 50 cm.
You will be expected hereafter to know and apply, in a variety of contexts, the definition given in this question. You need to know this definition word for word. If you try to apply the definition without using all the words it is going to cost you time and it will very likely diminish your performance. Briefly explain how you will ensure that you remember this definition.
Good student response: The first thing to remember is that the rate of change definition is the change of a divided by the change of B. I will make a note of this to report back to in the future.