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: The average rate of change of length (cm) with respect to time (sec) is 10 cm/5 seconds or 2 cm/sec. In this case, quantity A is 10 cm and quantity B is 5 seconds.
The change in quantity A is 10 cm and the change in quantity B is 5 seconds. Quantities A and B have multiple values, so it's not accurate to say that 'quantity A is 10 cm and quantity B is 5 seconds./
• 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 in this case would refer to the change in velocity which is 30cm/sec. Quantity B would refer to the change in clock time or 3 seconds. To find the average rate of change, you would divide (30cm/sec)/3 seconds giving 10 cm/sec^2..
quantity A is the velocity, not the change in velocity
change in velocity is change in quantity A
a similar statement can be made for quantity B.
• 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: Quantity A in the problem is associated with position change and must be solved for. Quantity B is given as 10 seconds and the average rate of change if given as 5cm/sec. In order to solve for quantity A, you would take 5cm/sec=A/10 sec. Solving for A you get, quantity A= 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.
answer/question/discussion: The definition states that the average rate of change is equal to the change in A divided by the change in B over an interval. This can be easily remembered by simply thinking about what rate of change is. You are finding the average rate of change IN RESPECT to B. This means that you need to find how much A changes in context to how much B changes. What other sorts of ways can this definition be remembered? I am a fan of mnemonic devices and other simple ways of memorizing fundamental material.
• 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: Application of this definition is fairly simple. You simply figure out which quantity is A and which quantity is B. Then you must find the change in each quantity over the given interval. This allows you to find the average rate of change of A in respect to the change in B. I will remember to apply this procedure by remembering the definition and using it to think about the problems. It is easy to infer a procedure from many definitions. It could also be remembered through a series of steps or a mnemonic device of some sort and would be interesting to see what one of these would look like.
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20 minutes
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Your answers are right; wee my notes on terminology.