#$&* PHY 241 Here is the definition of rate of change of one quantity with respect to another: The average rate of change of A with respect to B on an interval is average rate of change of A with respect to B = (change in A) / (change in B) Apply the above definition of average rate of change of A with respect to B to each of the following. Be sure to identify the quantity A, the quantity B and the requested average rate. If the position of a ball rolling along a track changes from 10 cm to 20 cm while the clock time changes from 4 seconds to 9 seconds, what is the average rate of change of its position with respect to clock time during this interval? answer/question/discussion (start in the next line): quantity A = change in position = 20 - 10 = 10 cm quantity B = change in time = 9 - 4 = 5 seconds average rate of change of position with respect to clock time = 10 cm / 5 seconds = 2 cm/sec #$&* 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 (start in the next line): quantity A = change of velocity = 40 - 10 = 30 cm / sec quantity B = change of time = 3 sec average rate of change of velocity with respect to time = (30 cm / sec) / 3 sec = 10 cm/sec^2 #$&* If the average rate at which position changes with respect to clock time is 5 cm / second, and if the clock time changes by 10 seconds, by how much does the position change? answer/question/discussion (start in the next line): quantity A = change in position = s quantity B = change in clock time = 10 sec change in position with respect to time = 5 cm/sec 5 = s / 10 => s = 50 cm #$&* 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): I will remember this definition by understanding the underlying principles of it. It is far more useful to work out the meaning of the definition, rather than memorizing it, so that not only can one recall it, but one can easily see why it works and how it applies to other problems. I understand that the change in a quantity A with respect to B is equal to the change in quantity A divided by the change in quantity B #$&* 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): 1. Distinguish each quantity A & B as some variable of change, and calculate it if possible using initial and final values 2. Recall that the change in A with respect to B = (change in A) / (change in B), and vice versa As previously stated, remembering this is a matter of understanding what it means, which is that the change of one variable A with respect to another variable B is equal to the change of the first divided by the change of the second