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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Problem 1 for Assignment 1
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:
Quantity A=the ball distance in cm
Quantity B=time in seconds
Average rate of change= (20-10)/(9-4)= 10/5= 2 cm
&#Quantity A is position, quantity B is clock time. The change in quantity A is (20 cm - 10 cm) = 10 cm, the change in position. The change in quantity B is 9 s - 4 s = 5 s, the change in clock time. So
Ave rate of change of position with respect to clock time = (change in position / change in clock time) = (10 cm/s) / (5 s) = 2 cm/s.
Note that the units are used at every step of the calculation. &#
• 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:
Quantity A=velocity of the ball
Quantity B=time in seconds
Average rate of change= (40-10)/(3-0)= 30/3= 10cm/sec
&#Quantity A is velocity, quantity B is clock time. The change in quantity A is (40 cm/s - 10 cm/s) = 30 cm/s. The change in quantity B is 3 s. So
Ave rate of change of velocity with respect to clock time = (change in velocity / change in clock time) = (30 cm/s) / (3 s) = 10 cm/s^2.
The unit calculation is (cm/s) / (s). Division is the same as multiplication by the reciprocal, so (cm/s) / (s) = (cm/s) * (1/s).
To multiply fractions we multiply numerators and multiply denominators, so (cm / s) * (1 / s) = (cm * 1) / (s * s) = cm / s^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:
Quantity A=position in cm
Quantity B=time in seconds
Average rate of change= 5cm/sec * 10sec= 50cm
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.
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This assignment took 10 minutes to finish.
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&#Let me know if you have questions. &#