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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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: We take the difference between the distances and divide it by the difference between the time. So we say (20-10)/(9-4) so we say 10/5 and that gives us a rate of change of 2cm per 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: We can see that the total increase of distance is 30cm over 3 seconds so we divide our distance by time and get a average rate of change of 10cm 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: We are given the average rate of change which is 5cm per second so we just have to use this information to get the total distance traveled over 10 seconds. So 10 times 5cm/second equals 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: I have taken note of the rate of change definition and I will refer to this note in the future.
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 first thing to remember is that the rate of change definition is the change of a divided by the change of B. I will make a note of this to report back to in the future.
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30 minutes
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I made a mistake and submited this form before I took the time to put all of the required information at the top of the form. I had two of them open so I could refer back to one of them, and I submitted the wrong one. I will try my best to not let this happen again.
You got most of this but you did miss the units on one part. See the following and let me know if you have any questions.
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?
We solve this by applying the definition of average rate of change.
10 cm and 20 cm are positions, so quantity A is position and quantity B is change in clock time.
The average rate of change of position with respect to clock time is therefore
ave rate = change in position / change in clock time = 10 cm / (5 s) = 2 cm/s.
The average rate of change of position with respect to clock time is by definition the average velocity.
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?
We solve this by applying the definition of average rate of change.
10 cm / sec and 40 cm / sec are velocities, so quantity A is velocity and quantity B is change in clock time.
The average rate of change of velocity with respect to clock time is therefore
ave rate = change in velocity / change in clock time = (30 cm / s) / (3 s) = 10 (cm/s) / (s) = 10 (cm/s) * (1/s) = 10 cm/s^2.
Note that this result is in units of cm/s^2, not cm/s.
The average rate of change of position with respect to clock time is by definition the average acceleration.
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?
The average rate of change of position with respect to clock time is
ave rate = (change in position) / (change in clock time). It follows that
change in position = ave rate * change in clock time, or more specifically
change in position = ave rate of change of position with respect to clock time * change in clock time. Thus
change in position = 5 cm/s * 10 s = 50 cm.