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: ->->->->->->->->->->->-> :
Well, the ball has moved 10cm total during the time period. It has moved from the 10cm mark to the 20cm mark, and 20 – 10 = 10cm. It also took the ball a total of 5 seconds to pass the two points. 9 seconds – 4 seconds = 5 seconds. In this case, quantity A would be the total distance traveled which is 10cm, and quantity B would be the time it took which was 5 seconds. Knowing this information, to find the average rate we must divide the total distance by the total time. So 10cm / 5seconds = an average rate of 2cm/second.
• 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: ->->->->->->->->->->->-> :
I’m a little unsure about how to go about solving this problem. I have drawn out a diagram of a ball passing two points on an incline in which it is moving 10cm/sec at the first point, and then 3 seconds later it is moving 40cm/sec. I would think to find the average rate of change, I must fist determine the actual distances along the track where the two points lie to determine the ‘quantity A.’ In order to do this, I subtracted 40cm by 10cm to get a 30cm change during the time period. Since ‘quantity B’ was already given to us as 3 seconds, I change formulate the average rate of change. So, 30cm / 3 seconds = an average rate of change of 10cm/second. But that just didn’t sound correct to me. It makes sense in terms of the ball is increasing its speed at a rate of 10cm/second for each second it rolls down the track, but it seemed strange that the average rate of change of the ball is the same rate the ball was rolling at the first interval.
Good thinking.
Note that 10 cm and 40 cm are not quantities given in this problem. You are given 10 cm/s and 40 cm/s, which are velocities, not to be confused with positions 10 cm and 40 cm.
• 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: ->->->->->->->->->->->-> :
In this case, we are given ‘quantity B’ as a change in 10 seconds. To get ‘quantity A,’ I had to find the distance the ball traveled. If it’s moving at an average of 5cm/second, and it has averaged that speed for 10 seconds, it must have moved 50cm. I get this quantity by multiplying 10sec. by 5cm/sec. which equals 50cm. To check this answer, I can simply say that if the ball has moved down the track 50cm, and it took that ball 10 seconds to accomplish this feet, its average rate of change down the track during the time interval was 5cm/second.
• 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: ->->->->->->->->->->->-> :
Well, this simply comes down to a matter of memorization. I must work on answering questions with respect to ‘quantity A,’ ‘quantity B,’ and ‘rate of change.’ You made it clear in the questions above to include those answers word-for-word. I will learn to answer the question by defining quantity A, B, and the rate of change, and that will in turn help me to learn the definition.
• 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: ->->->->->->->->->->->-> :
Like I said before, while answering the questions, I must clearly define what is quantity A, quantity B, and the rate of change. I have to apply the definition of the average rate of change when answering the questions. When answering questions, I usually start by including what I think the question asks of me. Then I go on to explain how I will go about finding both quantity A and quantity B. I then usually explain that in order to find the rate of change, I include the given definition of the change in A over the change in B. I then state what the average rate of change is for the given problem.
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This assignment took me around 2 hours to complete, but I did have some interruptions.
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&#Please compare your solutions with the expanded discussion at the link
Solution
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