question form

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2.85 seconds, 1.40 seconds, and 2.3 seconds cannot be clock times. The clock doesn't stop. Each clock time is greater than the preceding.

These can be time intervals.

The TIMER program introduced you to the distinction between clock times and time intervals. You should review that information.

The first column of the TIMER program numbers your clicks 1, 2, 3, 4, etc..

The second column gives you the clock times, which are the times since you started the TIMER program.

The third column gives you time intervals, each being the interval from the preceding clock time until the present clock time.

For example click number 4 will give you the clock time in the second column, and the interval between clock time #3 and clock time #4 in the third column.

There is often a long interval between starting the program and making your first meaningful click, so the clock times you get for a sequence of events will not start at zero. We often subtract the clock time of the first click from our subsequent clock times, to 'normalize' our clock times for a clock that did start at zero with the first click. This will change all the clock times, but not the time intervals. You should be sure you understand why this is. Note that this was also explained in the "Formatting Guidelines and Conventions" exercise.

Midpoint clock times were explained in the "Rotating Straw, Opposing Rubber Bands" exercise.

A midpoint clock time is the clock time halfway between the initial clock time for an interval and the final clock time during that interval. For example, for the interval between click #3 and click #4, the midpoint clock time would be halfway between clock time #3 and clock time #4. The time interval in the third column of the #4 row can more reasonably be associated with this midpoint clock time than with the initial or final clock time of the interval. A continually changing quantity calculated for the interval would most likely achieve its average value for that interval at the midpoint clock time (for example a velocity based on the time interval would more likely occur near the midpoint clock time of the interval than near the initial or final clock time).

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The following is copied from your "Formatting Guidelines and Conventions" document:

Suppose that the third column of the Timer program shows the numbers 3.7, 4.3, 5.2, 3.9, 4.3. Recall that the third line consists of the time intervals between clicks.

The clock time of the first click would be in the middle column. If necessary, briefly review the TIMER program, or the data you have obtained from that program.

We will define the 'first click' as the one that occurred at the beginning of the 3.7-second interval.

What would be the clock time relative to the first click of each of the four given numbers from the third line?

List these clock times in the first line in comma-delimited format. In the second line indicate the units of the numbers you have placed in the first line, and explain how you obtained the clock times.

your brief

discussion/description/explanation:

3.7, 8, 13.2, 17.1, 21.4

Added time between clicks.

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Your results are clock times, normalized so that the clock begins at 0.

Midpoint clock times are the clock times halfway between the consecutive clock times reported here.

3.7, 8, 13.2, 17.1, 21.4 are the clock times relative to the first click. You could expand this list to include the first click, which occurs at 0 on this clock, obtaining

0. 3.7, 8, 13.2, 17.1, 21.4

There are five intervals here, and there will be a midpoint clock time for each interval.

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If your numbers represent time intervals instead of clock times, then if we assume a clock that started with the first click the midpoint clock time for the first interval would indeed be be 1.425 seconds, occuring at the midpoint of the first interval which lasts from clock time 0 to clock time 2.85 seconds.

However the first interval lasts 2.85 seconds, so 2.125 seconds would not represent a clock time associated with the second interval, which doesn't start until the clock reaches 2.85 seconds.

What is the clock time at the beginning of the second interval, and at the end of that interval? What is the clock time at the midpoint of that interval?

The same questions should be applied to the third interval.

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Also from your Rotating Straw... document:

1 1465.164 1465.164

2 1466.188 1.023438

3 1467.133 .9453125

4 1468.684 1.550781

vAve Midpoint Clock Time

175.88 dps 0.52 s

190.41 dps 0.47 s

116.07 dps 0.78

For vAve, I divided 180 by the each time interval. Then I divided the time interval by 2 to find the midpoint.

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Your average velocities are fine.

However your midpoint clock times are not correct.

Your third time interval doesn't start until over 2 seconds after your first. So the midpoint of the third time interval could not be less than 2 seconds.

It appears you are reporting half the time interval as the midpoint clock time.

Also, clock times being the time read on a moving clock, clock times cannot decrease. Your second clock time is .47 s while your first is .52 s. This simply cannot occur.

Finally, your table depicts clock time vs. average velocity, not average velocity vs. clock time.

Please reread the information above regarding the midpoint clock time and make corrections accordingly.

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I've inserted fairly extensive notes to clarify the entire situation with clock times, time intervals and midpoint clock times.

I've also included relevant information from some of your submitted documents.

You are welcome to submit some of your data for the present experiment along with your reasoning and calculated midpoint clock times, just to be sure you're got it.

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