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course phy121
sept 15, 2014, 3:20pm
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, you find the average deviation from the overall average and square each of those values. After squaring all the values, you divide by the number of values minus 1. After all that you square root the entire equation to find the standard deviaition.
Sd= sqrt[{x1^2)+(x2^2)+(x3^2)/ (# of values-1)]
confidence rating #$&*: 3
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Question: State the given definition of the average rate of change of A with respect to B.
Briefly state what you think velocity is and how you think it is an example of a rate of change.
In reference to the definition of average rate of change, if you were to apply that definition to get an average velocity, what would you use for the A quantity and what would you use for the B quantity?
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Your solution:
To find the average velocity, you have to take the change of A and divide it by the change of B to obtain the average velocity. The velocity is the average speed during those intervals. For the A quantity, you would use the rate of change of the distance. For the B quantity, you would use the rate of change of the time during that interval.
Vav= (rate of change of A)/(rate of change of B)
confidence rating #$&*: 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:
The equation Vav= (change of A)/(Change of B) would work for tis problem, just need to rearrange it. Lets input some values to make it look easier. Average speed is 10m/s and the time interval was 2s. the equation would look like:
Vav*change of B (time)= change of A (distance)
10m/s*2s= distance
Distance= 20m
confidence rating #$&*: 3
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Given Solution:
** You multiply average speed * time interval to find distance moved.
For example, 50 miles / hour * 3 hours = 150 miles. **
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Self-critique (if necessary): OK
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Self-critique rating: OK
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Question: Given average speed and distance moved how do you find the corresponding time interval?
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Your solution:
When trying to find the time you rearrange the equation again.
Original equation= V=(distance moved)/(time interval)
Rearranged would be: Time= distance/speed
confidence rating #$&*: 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
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Self-critique rating: OK
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Question: Given time interval and distance moved how do you get average speed?
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Your solution:
To find the average speed you would take the distance/change in time.
confidence rating #$&*: 3
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Given Solution:
** Average speed = distance / change in clock time. This is the definition of average speed.
For example if we travel 300 miles in 5 hours we have been traveling at an average speed of 300 miles / 5 hours = 60 miles / hour. **
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Self-critique (if necessary): OK
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Self-critique rating: OK
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Question: A ball rolls from rest down a book, off that book and onto another book, where it picks up speed before rolling off the end of that book. Consider the interval that begins when the ball first encounters the second book, and ends when it rolls of the end of the book.
For this interval, place in order the quantities initial velocity (which we denote v_0), and final velocity (which we denote v_f), average velocity (which we denote v_Ave).
During this interval, the ball's velocity changes. It is possible for the change in its velocity to exceed the three quantities you just listed? Is it possible for all three of these quantities to exceed the change in the ball's velocity? Explain.
Note that the change in the ball's velocity is denoted `dv.
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Your solution:
V_Ave= (v_f at end of second book - v_0 at beginning of second book)/ (change in time from the end - beginning of book 2)
confidence rating #$&*: 3
@&
Good, but the question asked you to place a number of quantities in order.
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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:
Initial velocity: 4m/s
Change in velocity: 6m/s
Average velocity: (final+initial)/2= (10+4)/2= 14/2= 7m/s
Final velocity: 10m/s
No the change of velocity cannot exceed the other quantities because the final velocity is the maximum speed that it reached, which means there cannot be a value higher than that, especially the change in velocity.
confidence rating #$&*: 3
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Question: If the position of an object changes by 5.2 meters, with an uncertainty of +-4%, during a time interval of 1.3 seconds, with an uncertainty of +-2%, then
What is the uncertainty in the change in position in meters>
What is the uncertainty in the time interval in seconds?
What is the average velocity of the object, and what do you think ia the uncertainty in the average velocity?
(this last question is required of University Physics students only, but other are welcome to answer): What is the percent uncertainty in the average velocity of the object, and what is the uncertainty as given in units of velocity?
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Your solution:
Principle of physics student
confidence rating #$&*: 3
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Self-critique (if necessary):
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Self-critique rating:
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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_Ave= (v_f at end of second book - v_0 at beginning of second book)/ (change in time from the end - beginning of book 2)
confidence rating #$&*: 3
@&
Good, but the question asked you to place a number of quantities in order.
*@
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Question: If the velocity at the beginning of an interval is 4 m/s and at the end of the interval it is 10 m/s, then what is the average of these velocities, and what is the change in velocity?
List the four quantities initial velocity, final velocity, average of initial and final velocities, and change in velocity, in order from least to greatest.
Give an example of positive initial and final velocities for which the order of the four quantities would be different.
For positive initial and final velocities, is it possible for the change in velocity to exceed the other three quanities?
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Your solution:
Initial velocity: 4m/s
Change in velocity: 6m/s
Average velocity: (final+initial)/2= (10+4)/2= 14/2= 7m/s
Final velocity: 10m/s
No the change of velocity cannot exceed the other quantities because the final velocity is the maximum speed that it reached, which means there cannot be a value higher than that, especially the change in velocity.
confidence rating #$&*: 3
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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:
Principle of physics student
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
"
Self-critique (if necessary):
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Self-critique rating:
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&#Good responses. See my notes and let me know if you have questions. &#