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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Asst 1 Question 1
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:
A= ball position
B= clock time
Change in ball position/change in clock time= is the average rate of change of its position with respect to clock time during this interval. So, (20-10)/ (9-4) = (10)/ (5) = a rate of change of 2.
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• 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:
A= ball position
B= change in clock time
So, similar to above, the change in ball position/change in clock time= is the average rate of change of its velocity with respect to clock time during this interval. So, (40-10)/ (3) = (30)/ (3) = a rate of change of 10.
• 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:
A= ball position
B= change in clock time
C= average rate
We can take the equation, change in ball position/change in clock time= is the average rate of change of its position with respect to clock time during an interval and rearrange it so that the average rate is multiplied by the clock time to obtain the change in ball position. So, 5cm/second * 10 seconds= 50 cm change.
It's not quite correct to say that
'the average rate is multiplied by the clock time to obtain the change in ball position'.
The correct statement would be
'the average rate is multiplied by the change in clock time to obtain the change in ball position'.
This is an important distinction, since the first statement can in some common situations lead to serious errors.
Be sure you understand (as I believe you will) and let me know if you are in any way unsure of this.
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About half an hour or so.
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&#Good work. See my notes and let me know if you have questions. &#