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course Phy 121

9/6 8:51pm

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:

To find the standard deviation of a set of numbers: 1. Find the mean of the set. 2. Find the deviation from the mean of each individual number in the set. 3. Square the deviation of each individual number in the set. 4. Find the average of the squares of the deviations. (If there are less than 30 numbers in the set, be sure to use n-1 when dividing by the total number in set). 5. Take the square root of the ""average"" of the squares of the deviations. This gives you 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:

The average rate of change of A with respect to B is the Change in A divided by the Change in B.

Velocity is a change in position divided by a change in time. This is an example of a rate of change because it fits exactly the format of the average rate of change of A with respect to B.

confidence rating #$&*:3

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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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Self-critique (if necessary):OK

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Self-critique rating:OK

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

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Your solution:

Multiply the average speed by the time interval to find the distance moved.

confidence rating #$&*:3

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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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Self-critique (if necessary):OK

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Self-critique rating:OK

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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:

You can find the time interval by dividing the distance moved by the average speed.

confidence rating #$&*:3

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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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Self-critique (if necessary):Ok I need to get used to the notation of 'ds. ???Is that an accent mark? Is there a quick way to do that in Notepad???

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Self-critique rating:OK

@&
The ` mark is a 'back apostrophe'. It's all the way to the left on the number bank, just above the tab on most keyboards. The key has the ~ (called the 'tilda') and the `.

I use `d to indicate Delta, the capital Greek letter that looks like a triangle. You'll see an explanation of this in the first problems of the Introductory Problem Set.
*@

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

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Your solution:

Divide distance moved by time interval to get average speed.

confidence rating #$&*:3

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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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Self-critique (if necessary):OK

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Question: A ball rolls from rest down a book, off that book and onto another book, where it picks up speed before rolling off the end of that book. Consider the interval that begins when the ball first encounters the second book, and ends when it rolls of the end of the book.

For this interval, place in order the quantities initial velocity (which we denote v_0), and final velocity (which we denote v_f), average velocity (which we denote v_Ave).

During this interval, the ball's velocity changes. It is possible for the change in its velocity to exceed the three quantities you just listed? Is it possible for all three of these quantities to exceed the change in the ball's velocity? Explain.

Note that the change in the ball's velocity is denoted `dv.

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Your solution:

v_O, v_Ave, V_f

It would be possible for the change in velocity to exceed the inital velocity since the fact that there was a change means that it could be a change greater than the initial velocity. The change in velocity could exceed the average velocity if the change is indeed positive which would mean that the average is less than the overall change. The change in velocity could be greater than the final velocity if somehow the course was set up so that the first book was very steep and the second book was not steep at all and was goind very slowly at the end point. The change thus could be large and the final velocity smaller in comparison.

The intial velocity could exceed the change in velocity if the first book was very steep compared to the second. The ball could be moving very fast initially but not increase in velocity very much on the second book. In a similar set up, the average could be greater than the change if the ball did not change much at all in speed. The average speed could than exceed the change in speed. Lastly the final speed could exceed the change in speed if on a relatively level course the ball did not change much in velocity but started off rather fast and ended slightly faster. Here the final speed would exceed the change in speed.

confidence rating #$&*:2

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Question: If the velocity at the beginning of an interval is 4 m/s and at the end of the interval it is 10 m/s, then what is the average of these velocities, and what is the change in velocity?

List the four quantities initial velocity, final velocity, average of initial and final velocities, and change in velocity, in order from least to greatest.

Give an example of positive initial and final velocities for which the order of the four quantities would be different.

For positive initial and final velocities, is it possible for the change in velocity to exceed the other three quanities?

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Your solution:

The average velocity is 7m/s found by adding the two velocities together 4m/s + 10m/s =14m/s and dividing by 2 to get 7 m/s. The change in velocity is 10m/s - 4m/s which equals 6 m/s.

In order from lesast to greatest they would be: initial velocity, change in velocity, average of initial and final velocities, final velocity

If the initial velocity was 9m/s and the final velocity was 10 m/s, the order would change, It would be change in velocity, initial velocity, average of initial and final velocities, and final velocity.

If the the ball was losing speed it could have an intial velocity of 10 m/s and a final velocity of 1 m/s (both positive) The change in velocity would be 9 m/s and the average would be 5.5 m/s. Thus the change in velocity would be greater than the final, and the average velocities, but not the initial.

confidence rating #$&*:2

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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>

What is the uncertainty in the time interval in seconds?

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

(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:

The uncertainty in the change in position in meters is determined by using the formula %uncertainty = uncertainty/quantity *100%. Plug in some numbers and we get 4% = unc/5.2 meters *100%. Divide each side by 100% and we get: .04 =unc/5.2 meters. Multiply each side by 5.2 meters and we get+/- .21 meters uncertainty .

The uncertainty in the time interval in seconds is determined by using the formula %uncertainty = uncertainty/quantity *100%. Plug in some numbers and we get 2% = unc/1.3 *100%. Divide each side by 100% and we get: .02 =unc/1.3 s. Multiply each side by 1.3 s and we get+/- .026 seconds uncertainty .

The average velocity is 5.2m/1.3 s or 4m/s. We can add the uncertainties using the method of adding percents +/-4% + +/-2% gives us +/- 6% . 6%unc = unc/(4m/s) Divide each side by 100% and get .06=unc/(4m/s). Multiply both sides by 4m/s and get .24m/s or +/-.24

confidence rating #$&*:2

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Self-critique (if necessary):

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For this interval, place in order the quantities initial velocity (which we denote v_0), and final velocity (which we denote v_f), average velocity (which we denote v_Ave).

Note that the change in the ball's velocity is denoted `dv.

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Your solution:

v_O, v_Ave, V_f

confidence rating #$&*:2

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Question: If the velocity at the beginning of an interval is 4 m/s and at the end of the interval it is 10 m/s, then what is the average of these velocities, and what is the change in velocity?

List the four quantities initial velocity, final velocity, average of initial and final velocities, and change in velocity, in order from least to greatest.

Give an example of positive initial and final velocities for which the order of the four quantities would be different.

For positive initial and final velocities, is it possible for the change in velocity to exceed the other three quanities?

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Your solution:

The average velocity is 7m/s found by adding the two velocities together 4m/s + 10m/s =14m/s and dividing by 2 to get 7 m/s. The change in velocity is 10m/s - 4m/s which equals 6 m/s.

In order from lesast to greatest they would be: initial velocity, change in velocity, average of initial and final velocities, final velocity

confidence rating #$&*:2

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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>

What is the uncertainty in the time interval in seconds?

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

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Your solution:

confidence rating #$&*:2

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Self-critique (if necessary):

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For this interval, place in order the quantities initial velocity (which we denote v_0), and final velocity (which we denote v_f), average velocity (which we denote v_Ave).

Note that the change in the ball's velocity is denoted `dv.

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Your solution:

v_O, v_Ave, V_f

confidence rating #$&*:2

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Question: If the velocity at the beginning of an interval is 4 m/s and at the end of the interval it is 10 m/s, then what is the average of these velocities, and what is the change in velocity?

List the four quantities initial velocity, final velocity, average of initial and final velocities, and change in velocity, in order from least to greatest.

Give an example of positive initial and final velocities for which the order of the four quantities would be different.

For positive initial and final velocities, is it possible for the change in velocity to exceed the other three quanities?

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Your solution:

The average velocity is 7m/s found by adding the two velocities together 4m/s + 10m/s =14m/s and dividing by 2 to get 7 m/s. The change in velocity is 10m/s - 4m/s which equals 6 m/s.

In order from lesast to greatest they would be: initial velocity, change in velocity, average of initial and final velocities, final velocity

confidence rating #$&*:2

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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>

What is the uncertainty in the time interval in seconds?

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

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Your solution:

confidence rating #$&*:2

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Self-critique (if necessary):

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Query_1

&#Good responses. See my notes and let me know if you have questions. &#