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.
** **
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” is the rate of change in distance (10cm) and “B” is the rate of change of the clock (5sec). Average rate of change is 2cm/1sec.< /p>
The definition says that
average rate of change of A with respect to B = (change in A) / (change in B),
If A is the rate of change in position and B the rate of change in clock time, then by this definition we would have
average rate of change of rate of change in position with respect to rate of change of clock time = (change in rate of change of position) / (change in rate of change in clock time).
However what we want here is the average rate of change of position with respect to clock time. So the A quantity is simply position, and the B quantity is simply clock time.
• 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: ->->->->->->->->->->->-> : Quantity A is 30cm/second and B is 3 seconds. So, the ball is gaining a velocity of 10cm/sec for each second that it is rolling.
Your final answer is correct, and your reasoning process is good, but you have not correctly labeled all the quantities.
Quantity A is velocity, and quantity B is clock time.
30 cm/s is the change in velocity, which you have correctly obtained by subtracting 10 cm/s from 40 cm/s.
However quantity A being velocity, and 30 cm/s being change in velocity, we cannot say that quantity A is 30 cm/s.
30 cm/s is the change in A, not the A quantity itself.
3 seconds is a time interval, which is an interval between two clock times, or a change in clock time. It is not a clock time, so 3 seconds is not the B quantity.
3 seconds is the change in the B quantity, not the B quantity itself.
• 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/second(A) multiplied by 10 seconds(B) equals a position change of 50cm.
• 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: ->->->->->->->->->->->-> : This definition is pretty much common sense, it is totally self-explanatory. It is one that we use in everyday life, but I will still try to know it to the best of my abilities.
• 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 average rate of change of A with respect to B is just the change in A divided by the change in B. Just as before, this procedure is one used regularly and I am pretty sure I will know it for a long time.
** **
About 10 minutes
** **
Basically good work, but you didn't always label your quantities correctly, so see my notes above and below.
It's very important to label the A and the B quantities carefully and correctly. If you get in the habit of labeling these quantities with the correct terms, you will more quickly expand your understanding of this important definition and your ability to apply it correctly in the many different situations you will encounter in this course.
It is very important in all fields to apply and understand the words and phrases used in definitions and descriptions.