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.
Question: `q001. The following is a list of terms associated with the definitions of average velocity and average acceleration:
Below are listed four quantities that might be observed or calculated in an experiment:
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.
Your solution:
Confidence Assessment:
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'.
Self-critique (if necessary):
Self-critique rating:
Question: `q002. The following is a list of terms used in the analysis of uniformly accelerated motion.
Below are listed four quantities that might be observed or calculated in an experiment:
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:
Your solution:
Confidence Assessment:
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'.
Self-critique (if necessary):
Self-critique rating:
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:
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:
Your solution:
Confidence Assessment:
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).
Self-critique (if necessary):
Self-critique rating:
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:
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:
Your solution:
Confidence Assessment:
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).
Self-critique (if necessary):
Self-critique rating: