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course phy 121

11/22/13 11:21 pm

ph1 query 1

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Question: `qExplain in your own words how the standard deviation of a set of numbers is calculated.

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Your solution:

Find the mean of the entire set by adding the data values together and dividing by the number of data in the set. Then for each sample data, find the difference between the sample data and the set’s mean value and take the absolute value, these are the deviations. Then square the deviations. Next find the average of the deviations by adding them together and dividing by the number of sample data if more than 30 sample data are used, and if less than 30 sample data are used, then divide by 1 less than the number of sample data used. Then take the square root of this quotient to get the standard deviation.

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Question: State the given definition of the average rate of change of A with respect to B.

Briefly state what you think velocity is and how you think it is an example of a rate of change.

In reference to the definition of average rate of change, if you were to apply that definition to get an average velocity, what would you use for the A quantity and what would you use for the B quantity?

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Your solution:

Average rate of change of A with respect to B is found by the formula , change in A/change in B.

Velocity is the speed at which an object travels in a given direction over a given time interval so it is the rate of change of the position of an object. Velocity is a rate of change because you could find the average rate of change in velocity with respect to clock time by taking the change in position/change in clock time.

Qty A would be change in position and qty B would be change in clock time

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Given Solution:

A rate is a change in something divided by a change in something else.

This question concerns velocity, which is the rate of change of position: change in position divided by change in clock time. **

NOTE ON NOTATION

Students often quote a formula like v = d / t. It's best to avoid this formula completely.

The average velocity on an interval is defined as the average rate of change of position with respect to clock time. By the definition of average rate, then, the average velocity on the interval is v_ave = (change in position / change in clock time).

• One reason we might not want to use v = d / t: The symbol d doesn't look like a change in anything, nor does the symbol t. Also it's very to read 'd' and 'distance' rather than 'displacement'.

• Another reason: The symbol v doesn't distinguish between initial velocity, final velocity, average velocity, change in velocity and instantaneous velocity, all of which are important concepts that need to be associated with distinct symbols.

In this course we use `d to stand for the capital Greek symbol Delta, which universally indicates the change in a quantity. If we use d for distance, then the 'change in distance' would be denoted `dd. It's potentially confusing to have two different d's, with two different meanings, in the same expression.

We generally use s or x to stand for position, so `ds or `dx would stand for change in position. Change in clock time would be `dt. Thus

v_Ave = `ds / `dt

(or alternatively, if we use x for position, v_Ave = `dx / `dt).

With this notation we can tell that we are dividing change in position by change in clock time.

For University Physics students (calculus-based note):

If x is the position then velocity is dx/dt, the derivative of position with respect to clock time. This is the limiting value of the rate of change of position with respect to clock time. You need to think in these terms.

v stands for instantaneous velocity. v_Ave stands for the average velocity on an interval.

If you used d for position then you would have the formula v = dd / dt. The dd in the numerator doesn't make a lot of sense; one d indicates the infinitesimal change in the other d.

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Question: Given average speed and time interval how do you find distance moved?

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Your solution:

If you want to find the distance moved, and you are given average speed and the time interval you are wanting ot know the change in position.

We know the formula for velocity is change in position/change in clock time so we could solve this for so solving the formula for change in position gives us

Change in position = velocity * change in time

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Given Solution:

** You multiply average speed * time interval to find distance moved.

For example, 50 miles / hour * 3 hours = 150 miles. **

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Question: Given average speed and distance moved how do you find the corresponding time interval?

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Your solution:

The formula is velocity = change in position / change in clock time

If we are given the avg speed (velocity) and the change in position, we solve for change in clock time which is

Velocity * change in clock time = change in position

Change in clock time = change in position / velocity

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Given Solution:

** time interval = distance / average speed. For example if we travel 100 miles at 50 mph it takes 2 hours--we divide the distance by the speed.

In symbols, if `ds = vAve * `dt then `dt = `ds/vAve.

Also note that (cm/s ) / s = cm/s^2, not sec, whereas cm / (cm/s) = cm * s / cm = s, as appropriate in a calculation of `dt. **

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Question: Given time interval and distance moved how do you get average speed?

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Your solution:

If you have time interval and distance moved to get avg speed you used

Change in position /change in clock time

So distance moved/time interval

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Given Solution:

** Average speed = distance / change in clock time. This is the definition of average speed.

For example if we travel 300 miles in 5 hours we have been traveling at an average speed of 300 miles / 5 hours = 60 miles / hour. **

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Question: If the position of an object changes by 5.2 meters, with an uncertainty of +-4%, during a time interval of 1.3 seconds, with an uncertainty of +-2%, then

What is the uncertainty in the change in position in meters> 5.2 *+- .04 = .208 or -.208

What is the uncertainty in the time interval in seconds? 1.3 * +- .02 = -.026 or .026

What is the average velocity of the object, and what do you think ia the uncertainty in the average velocity?

Velocity = change in position / change in clock time

The avg velocity is 5.2/1.3 = 4

Uncertainty

(5.2 + .208)/(1.3+.026) = 4.078 or

(5.2-.208)/(1.3-.026)=3.918 or

(5.2 + .208)/(1.3-.026) = 4.245 or

(5.2+.208)/(1.3 + .026)= 4.078

(this last question is required of University Physics students only, but other are welcome to answer): What is the percent uncertainty in the average velocity of the object, and what is the uncertainty as given in units of velocity?

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Your solution:

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