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phy 201
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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: ->->->->->->->->->->->-> (start in the next line):
(20cm-10cm)/(9s/4s)=(10cm/5s)=2cm per second is the average rate of change
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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):
(30cm/second / 3seconds) = 10 cm/s is the average rate of change
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30 cm/s / 3 would equal 10 cm/s.
However 30 cm/s / (3 s) would not be 10 cm/s. The 10 is correct, but the unit cm/s is not the correct unit that results from the calculation.
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