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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:
Avg rate of change of A (position) with respect to B (clock time) = (change in position) / (change in clock time) =
(20cm - 10cm) / (9sec - 4sec) =
10cm / 5 sec = 2cm/sec
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:
Avg rate of change of A (velocity) with respect to B (clock time) =
(change in velocity) / (change in clock time) =
(40 cm/sec - 10 cm/sec) / 3 sec =
(30 cm/sec) / 3 sec =
(10cm/sec) / sec
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:
Avg rate of change of A (position) with respect to B (clock time) = 5 cm/sec
5cm/sec = X/10sec where X = position change
X = 50cm
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20 mins
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