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Phy 121
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.
** CQ_1_01.1_labelMessages **
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: ->->->->->->->->->->->-> n/discussion (start in the next line):
The quantity A is the position of the ball. The quantity B is the clock time. So we calculate the change in A or position and divide it by the change in B or time to get the average rate of change of A with respect to B.
(20cm -10cm)/(9s -4s) = 10cm/5s = 2cm/s
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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: ->->->->->->->->->->->-> scussion (start in the next line):
The quantitiy A is the velocity of the ball. The quantity B is the clock time.
So we calculate the change in velocity (A)and divide it by the change in clock time (B) to get the average rate of change of A with respect to B on an interval.
.
(40 cm/s - 10cm/s)/3s = (30cm/s)/s = 30cm/s^2
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In the second step you appear to have eliminated the 3 s in the denominator, replacing it with just s.
The result would be 30 cm/s / (3 s) = 10 cm/s^2, as I'm sure you realize.
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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: ->->->->->->->->->->->-> scussion (start in the next line):
Quantity A is unknown. Quantity B is the clock time. Change in A divide by Change in B = average rate of change of A with respect to B on an interval/
We know average rate of change of A with respect to B on an interval is 5 cm/s and we know the Change in B is 10 seconds. We have enough information to solve for the change in position (change in A)
Change A / 10 s = 5 cm/s. Multiply both sides by 10 s. We get Change A = 50 cm
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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: ->->->->->->->->->->->-> scussion (start in the next line):
I will remember it by repeating it in problems where it applies from here on out. That practice should ensure that I remember it.
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Very good, but check my note on an apparent oversight in one of your calculations.
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