ic_ kinetic qa

course phy 201

Origionally submitted Sunday afternoon, this is a resubmit (1004 am on Wednesday, Sept 30)

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution.

If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

060. Special QA on Kinematic Quantities.

Kinematic Quantities

This exercise is designed to help you understand and identify the basic kinematic quantities (the quantities associated with the definitions of average velocity and average acceleration on an interval) and their units, and/or to check your understanding.

If you have been recommended for this assignment in notes on your homework, you should review the information below and use it to answer the questions in this document:

If you are using this for a check-up on your understanding of the quantities, you may use this document in any way you wish. You may simply start answering the questions, and check yourself against the given solutions. If you wish to submit your work you may do so.

First be sure we understand how the units of position, velocity, acceleration and clock time are related:

The units of velocity:

A velocity is a rate of change of position with respect to clock time, which is (change in position) / (change in clock time).

The units of position are units of distance or displacement.

The change in position is obtained by subtracting the initial position from the final position.

When two quantities with the same units are subtracted, the rules of algebra dictate that the result has the same units.

So change in position has units of displacement.

Time is a fundamental undefined quantity:

The units of clock time are units of time.

The change in clock time is obtained by subtracting the initial clock time from the final clock time.

When two quantities with the same units are subtracted, the rules of algebra dictate that the result has the same units.

So change in clock time has units of time.

It follows that

the units of velocity are units of distance divided by units of time.

The units of acceleration:

An average acceleration is a rate of change of velocity with respect to clock time, which is (change in velocity) / (change in clock time).

The units of velocity are units of distance divided by units of time.

The change in velocity is obtained by subtracting the initial velocity from the final velocity.

When two quantities with the same units are subtracted, the rules of algebra dictate that the result has the same units.

So change in velocity has units of velocity.

As seen before, change in clock time has units of time.

So when we divide change in velocity by change in clock time we get units of distance divided by squared units of time:

For example if position is measured in meters and time in seconds, the units of acceleration are meters / second^2.

Thus

The units of acceleration are units of distance divided by squared units of time:

To summarize:

Units of position are units of distance or displacement. Examples are meters, centimeters, kilometers, nanometers, etc.

Units of velocity are units of distance or displacement divided by units of clock time. Examples are meters / second, kilometers / hour, nanometers / millisecond, etc..

Units of acceleration are units of distance or displacement divided by squared units of clock time. Examples are centimeters / second^2, miles / hour^2, etc..

To emphasize:

If a quantity has units of distance divided by units of clock time, it can be some sort of a velocity (it could be an initial, final, change in, average, or instantaneous velocity). It can't be a position or an acceleration or a clock time because it doesn't have the units of those quantities.

If a quantity has units of distance, it can be a position or a change in position. It can't be a velocity or an acceleration or a clock time because it doesn't have the units of those quantities.

If a quantity has units of clock time, it can be a clock time or a change in clock time or a time interval. It can't be a position or a velocity or an acceleration because it doesn't have the units of those quantities.

If a quantity has units of distance divided by squared units of time, it can be an average or instantaneous acceleration. It can't be a velocity or an position or a clock time, etc., because it doesn't have the units of those quantities.

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Question: `q001. The following is a list of terms associated with the definitions of average velocity and average acceleration:

Position

Velocity

Acceleration

Clock time

Average velocity

Average acceleration

Rate of change of position with respect to clock time

Time interval

Change in position

Rate of change of velocity with respect to clock time

Change in velocity

Change in clock time.

Below are listed four quantities that might be observed or calculated in an experiment:

30 cm / s

50 s

90 cm/s^2

40 cm * s

Identify each of these quantities by listing each, followed by the terms that might apply to each, and your justification for each set of answers.

(For example, if one of the quantities given had been 50 km / hr^3, someone might answer as follows (note that the sample answer is not a good answer; it's intended only to demonstrate the format of the answer):

50 km / hr^3: 1, 4, 7, 12. Justification: All these things have units of distance or time, and so does the question.

meaning that 50 km/hr^3 is a position, a clock time, a rate of change of position with respect to clock time, and a time interval.

These answers are completely inconsistent, and in fact all a incorrect, but this is the format expected in your answers).

Note that 'none of the above' is a possible answer; that is, some quantities might not have the units of any of the quantities in the list.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

30 cm/s could be a measurment of velocity or average velocity because it is obviously the product of a change in position with respect to change in clock time which is the definition of velocity. Also 30 cm/s could be the change in velocity that an object experienced. The units cm/s are consistant with the value of some measurement of velocity so options 2,5, 7 and 11 could all apply to this quantity.

50 s could be a clock time (option 4), a time interval (option 8) or a change in clock time (option 12). All these options are possible because the unit of measurement is seconds which we all know is used to measure clock time. All these options given are related to clock time measurement. There are other options that include clock time with other measurments but these are the only ones that involve only clock time.

90 cm/s^2 could be the acceleration (option 3), average acceleration (option 6), or change in velocity with respect to clock time (option 10). This is because average accelerations definition is the change in velocity with respect to clock time. For this example it is fairly obvious that the velocity was measured in cm/s then when that was divided by clock time in seconds you get the cm/s^2 that is in this value.

40 cm*s none of the above

confidence rating: very confident

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Given Solution:

30 cm/s has units of cm / s, which are units of displacement divided by units of time. Thus 30 cm/s has units of velocity. So 30 cm/s it could be any of the quantities 2, 5, 7, or 11 (velocity, average velocity, rate of change of position with respect to clock time (which is the definition of average velocity), or change in velocity).

50 s has units of s, or seconds, which are units of time. So 50 s can possibly represent any of the quantities 4, 8 or 12 (a clock time, a time interval, or a change in clock time).

90 cm/s^2 has units of distance divided by squared units of time. Thus 90 cm/s^2 has units of acceleration. So 90 cm/s^2 could be any of the quantities 3, 6 of 10 (acceleration, average acceleration, or rate of change of velocity with respect to clock time (which is the definition of average acceleration).

40 cm * s has units of distance multiplied by units of time. None of the important kinematic quantities (i.e., the quantities associated with the definitions of average velocity and average acceleration) have units of cm * s, and none of the quantities in the list have these units. So the answer here is 'none of the above'.

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Self-critique (if necessary): not necessary

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Self-critique rating: not necessary

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Question: `q002. The following is a list of terms used in the analysis of uniformly accelerated motion.

Time interval

Velocity

Rate of change of velocity with respect to clock time

Average acceleration

Average velocity

Clock time

Rate of change of position with respect to clock time

Change in clock time

Change in position

Acceleration

Change in velocity

Position

Below are listed four quantities that might be observed or calculated in an experiment:

20 km / year^2

30 miles

42 nanometers / picosecond

15 cm^2 / s

Identify each of these quantities by listing each, followed by the terms that might apply to each, and your justification for each set of answers:

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

20 km/year^2 involves the change in position divided by the change in clock time, which is velocity, and then dividing that quantity again by the clock time. Making a long story short it is the change in velocity with respect to clock time. This is the definition of acceleration. Knowing this we can determine that this quantity can represent options 3,4 and 10 (rate of change of velocity with respect to clock time, average acceleration and acceleration)

30 miles has the unit of miles, which is used to measure distances. Knowing this we can determine that this quantity could represent options 9 or 12 (change in position or position)

42 nanometers/ picosecond has units that represent the change of position with respect to clock time which is the definition of velocity. Knowing this we can determine that this quantity could represent options 2,5,7 or 11 (velocity, average velocity, rate of change of position with respect to clock time, or change in velocity.)

15 cm^2/ s dose not have units that match any of the given choices. So this quantity represents none of the above

confidence rating: very confident

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Given Solution:

20 km / year^2 has units of distance (km) divided by squared units of time (year^2), so it has units of acceleration. It could therefore represent any of the quantities 3 (rate of change of velocity with respect to clock time, which is the definition of average acceleration), 4 (average acceleration) or 10 (acceleration).

30 miles has units of miles, which is a measure of distance or displacement. It could therefore represent either of the quantities 9 (change in position) or 12 (position).

42 nanometers / picosecond has units of distance (nanometers) divided by units of time (picoseconds), which give it units of velocity. It can therefore represent any of the quantities 2 (velocity), 5 (average velocity), 7 (rate of change of position with respect to clock time, which is the definition of average velocity) or 11 (change in velocity).

15 cm^2 / s has units of squared distance (cm^2) divided by units of time (s). None of the quantities associated with the definitions of average velocity or average acceleration has units of squared distance divided by time, so this quantity is not associated with the analysis of motion. The correct answer would be 'none of the above'.

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Self-critique (if necessary): not necessary

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Self-critique rating: not necessary

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Question: `q003. The following is a list of terms used in the analysis of uniformly accelerated motion.

Initial velocity on an interval

Final velocity on an interval

Average velocity on an interval

Change in velocity on an interval

Average acceleration on an interval

Change in position on an interval

Change in clock time on an interval

Displacement on an interval

Below are listed four quantities that might be observed or calculated in an experiment:

20 m / s^2

40 s

35 cm / s

70 cm

Identify each of these quantities by listing each, followed by the terms that might apply to each, and your justification for each set of answers:

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

20 cm/s^2 has units that are consistant with the units used when measuring acceleration. So this makes it clear that this particular quantitiy could represent the average acceleration on the interval (option 5)

40 s has the unit of seconds that is used to measure clock time. This leads one to believe that this quantity could represent the change in clock time on the intercal (option 7)

35 cm/s has the unit if cm/s which is used for velocity measurements this means that this quantity could represent the change in velocity on the interval (option 4), the average velocity on the inteval (option 3), the final velocity on the interval (option 2) or the initial velocity on the interval (option 1)

70 cm has the unit of cm which is used to measure distance or position of an object. So this quantity could represent the displacement on the interval (option 8) or the change in position on the interval (option 6).

confidence rating: very confident

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Given Solution:

20 m/s^2 has units of distance (m) divided by squared units of time (s^2), so it has units of acceleration. It could therefore represent quantity 5 (average acceleration on an interval).

40 s has units of s, or seconds, which are units of time. So 50 s can possibly represent any of the quantities 4, 8 or 12 (a clock time, a time interval, or a change in clock time).

35 cm/s has units of distance (cm) divided by units of time (s), which give it units of velocity. It can therefore represent any of the quantities 1 (initial velocity on an interval), 2 (final velocity on an interval), 3 (average velocity in an interval), or 4 (change in velocity in an interval).

70 cm has units of cm, which is a measure of distance or displacement. It could therefore represent the quantity 6 (change in position on an interval) or the quantity 8 (displacement on an interval, which is defined as the change in position on the interval).

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Self-critique (if necessary): not necessary

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Self-critique rating: not necessary

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Question: `q004. The following is a list of terms used in the analysis of uniformly accelerated motion.

Change in clock time on an interval

Initial velocity on an interval

Change in position on an interval

Average velocity on an interval

Displacement on an interval

Average acceleration on an interval

Final velocity on an interval

Change in velocity on an interval

Below are listed four quantities that might be observed or calculated in an experiment:

20 m / s

40 cm

35 cm / s^2

70 s

Identify each of these quantities by listing each, followed by the terms that might apply to each, and your justification for each set of answers:

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

20 m/s has units that are used in measuring velocity. This means that this quanity could represent the initial velocity on the interval (option 2), the average velocity on the interval (option 4), the final velocity on the interval (option 7) or the change in velocity on the intercval (option 8)

40 cm has the unit cm which is used to measure position or distance. So this quantity could represent the change in position on the time interval (option 3) or the displacement on an interval (option 5)

35 cm/s^2 has the unit cm/s^2 which is used when talking about acceleration. So this quantity could represent the average acceleration on the interval (option 6)

70 s has the unit of seconds which is used to measure clock time. So this quantity could represent the change in clock time on the interval (option 1).

confidence rating: very confident

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Given Solution:

35 cm/s^2 has units of distance (cm) divided by squared units of time (s^2), so it has units of acceleration. It could therefore represent quantity 6 (average acceleration on an interval).

70 s has units of s, or seconds, which are units of time. So 50 s can possibly represent any of the quantities 4, 8 or 12 (a clock time, a time interval, or a change in clock time).

20 m/s has units of distance (m) divided by units of time (s), which give it units of velocity. It can therefore represent any of the quantities 2 (initial velocity on an interval), 7 (final velocity on an interval), 4 (average velocity in an interval), or 8 (change in velocity in an interval).

40 cm has units of cm, which is a measure of distance or displacement. It could therefore represent the quantity 3 (change in position on an interval) or the quantity 5 (displacement on an interval, which is defined as the change in position on the interval).

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Self-critique (if necessary):not necessary

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Self-critique rating: not necessary

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&#Very good responses. Let me know if you have questions. &#