PHY231
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: ->->->->->->->->->->->-> : This question is looking for rate of change of the ball with respect to time. The ball travels a total of 10cm (20cm – 10cm) over a period of 5 seconds (9 seconds – 4 seconds). To find the rate of change with respect to time:
10cm/5s = 2cm/s
• 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: ->->->->->->->->->->->-> : The velocity changes a total of 30cm/s over the course of 3 seconds. The rate of change with respect to time during this period would be 30cm/s / 3s = 10cm/s/s or a change of 10cm per second per second.
• 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: ->->->->->->->->->->->-> : At 5cm/s over a period of 10 seconds the position would change 10s * 5cm/s = 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: ->->->->->->->->->->->-> : The definition for rate of change is a basic formula used in mathematics. I have used this through many classes and will continue to use it on an almost daily basis.
• 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 procedure for applying the definition of a rate of change is as follows. Find the data you need to compute. Decide which element you need to find the solution with respect to. Make any conversions to measurements. Solve.
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15 minutes
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Overall good, but you didn't always connect your work to the definition of average rate, and you had some units errors.
&#Please compare your solutions with the expanded discussion at the link
Solution
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