course Phy 121
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 (start in the next line):
Changes in the position is from 10 cm to 20 cm, meaning it changed 10 cm. Change in time is from 4 seconds to 9 seconds, meaning it changed 5 seconds. Change in position over change in time means the average rate of change is 10cm/5seconds, or 2cm/second.
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• 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 (start in the next line):
The velocity change is 30 cm/second in 3 seconds, or 30cm/second*3 seconds, meaning an average velocity change of 10cm/second.
Good, but be sure you have the words right. It's an average rate of velocity change, with respect to clock time, of 10cm/second. The 'rate' terminology is necessary.
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• 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 (start in the next line):
An object traveling 5cm/second for 5 seconds would end up traveling 25cm
the given time interval is 10 seconds
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• 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 (start in the next line):
Change in A over Change in B gives you the average rate of change……. This makes sense if you think that speed (or the rate of change of speed) is divided by the amount of time it is changing (or the change in time), gives you how much it changes per unit of time or distance…..
#$&*
• You are asked in this exercise to apply the definition, and given a general procedure for doing so. Briefly outline the procedure for applying this definition, and briefly explain how you will remember to apply this procedure.
answer/question/discussion (start in the next line):
If something has a rate (or as speed or travel “time” over a time period) and this rate in changing, then using the average rate of change formula can determine the time it takes for this object to travel a certain distance per specified unit of time. What helps me the most, is writing down what I know, then writing down what I need to know, and then drawing a drawing of (for example) a ball rolling down an incline, the start time and rate and the ending time and rate and just looking at it to see what’s missing and what I have to figure out to get the answer.
"
Seed questions need to be submitted using the form from which you get them. Each question is presented within its own form. This is important; if I don't notice, and that's not the sort of detail I'm focusing on, your submission could get misrouted or connected to the wrong link.
&#See any notes I might have inserted into your document. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
#$&*
*&$*&$
course Phy 121
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 (start in the next line):
Changes in the position is from 10 cm to 20 cm, meaning it changed 10 cm. Change in time is from 4 seconds to 9 seconds, meaning it changed 5 seconds. Change in position over change in time means the average rate of change is 10cm/5seconds, or 2cm/second.
#$&*
• If the velocity of a ball rolling along a track changes from 10 cm / second to 40 cm / second during an interval during which the clock time changes by 3 seconds, then what is the average rate of change of its velocity with respect to clock time during this interval?
answer/question/discussion (start in the next line):
The velocity change is 30 cm/second in 3 seconds, or 30cm/second*3 seconds, meaning an average velocity change of 10cm/second.
Good, but be sure you have the words right. It's an average rate of velocity change, with respect to clock time, of 10cm/second. The 'rate' terminology is necessary.
#$&*
• 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 (start in the next line):
An object traveling 5cm/second for 5 seconds would end up traveling 25cm
the given time interval is 10 seconds
#$&*
• You will be expected hereafter to know and apply, in a variety of contexts, the definition given in this question. You need to know this definition word for word. If you try to apply the definition without using all the words it is going to cost you time and it will very likely diminish your performance. Briefly explain how you will ensure that you remember this definition.
answer/question/discussion (start in the next line):
Change in A over Change in B gives you the average rate of change……. This makes sense if you think that speed (or the rate of change of speed) is divided by the amount of time it is changing (or the change in time), gives you how much it changes per unit of time or distance…..
#$&*
• 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 (start in the next line):
If something has a rate (or as speed or travel “time” over a time period) and this rate in changing, then using the average rate of change formula can determine the time it takes for this object to travel a certain distance per specified unit of time. What helps me the most, is writing down what I know, then writing down what I need to know, and then drawing a drawing of (for example) a ball rolling down an incline, the start time and rate and the ending time and rate and just looking at it to see what’s missing and what I have to figure out to get the answer.
"
Seed questions need to be submitted using the form from which you get them. Each question is presented within its own form. This is important; if I don't notice, and that's not the sort of detail I'm focusing on, your submission could get misrouted or connected to the wrong link.
&#See any notes I might have inserted into your document. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
#$&*
*&$*&$