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 the ball is 2 cm/second. This is found by taking the change in distance our A quantity: 20 cm- 10 cm= 10 cm. Then the change in time our B quantity: 9 seconds- 4 seconds = 5 seconds. Next we divide the two values. 10 cm / 5 seconds = 2 cm/ 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: Since the ball has increased in velocity we must find the difference between the two. 40 cm/sec – 10 cm/sec = 30 cm/sec. Next we must take note of the time in which it occurred. Since it took 3 seconds, we must divide the rate by the time change. 30 cm/sec / 3 = 10 cm/sec. The ball is increasing in velocity by 10 cm per second.
your units in the last answer are not correct, but your reasoning is very sound and correct
(cm / sec) / sec gives you cm/sec^2
• 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: Since we are given a rate of change and a time period we must now multiply the two values. The object is moving 5 cm/sec multiplied by the amount of time 10 seconds. This will cancel out the value of seconds from the final answer. 5 cm/sec X 10 sec = 5 cm X 10= 50 cm. The object has moved 50 centimeters.
• 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: To remember this I will keep in mind that any object that is moving must be compared to an amount of time. If it is not compared then velocity cannot be measured. In other cases the term rate will be the mind spark that will help me to remember than A is always compared to B. It is their changes in relation to one another.
• 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: To determine the average rate of change in an object with respect to a variable, we must first determine the A and B values. The A value is the change in the object itself. The B value is the change in the variable we are using for a comparison. Such that if a ball moves 2 cm in 20 seconds we must take the A value of 2 cm and divide it by the B value of 20 sec. 2 cm/ 20 sec =1/10 cm/sec.
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15 minutes.
&#Your work looks good. See my notes. Let me know if you have any questions. &#