course Phys 201
007. `query 7Question: **** `qDescribe the flow diagram you would use for the uniform acceleration situation in which you are given v0, vf, and `dt.
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Your solution:
Vo Vf dt
dv or vAve
ds (dv and dt)
a(dv and dt)
Confidence Assessment: 3
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Given Solution:
We start with v0, vf and `dt on the first line of the diagram.
We use v0 and vf to find Vave, indicated by lines from v0 and vf to vAve.
Use Vave and 'dt to find 'ds, indicated by lines from vAve and `dt to `ds.
Then use `dv and 'dt to find acceleration, indicated by lines from vAve and `dt to a. **
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Self-critique (if necessary):
Self-critique Rating:3
Question: **** Describe the flow diagram you would use for the uniform acceleration situation in which you are given `dt, a, v0
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Your solution:
dt a vo
\ l /
ds
\ l /
vf
\ l
vAve and dv
Confidence Assessment: 3
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Given Solution:
Student Solution: Using 'dt and a, find 'dv.
Using 'dv and v0, find vf, indicated by lines from `dv and v0 to vf.
Using vf and v0, find vAve, indicated by lines from vf and v0 to vAve
Using 'dt and vAve, find 'ds, indicated by lines from `dt and vAve to `ds.
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Self-critique (if necessary): i dont understand how you answer matches up with the question.
Self-critique Rating:2
Question: **** Explain in detail how the flow diagram for the situation in which v0, vf and `dt are known gives us the two most fundamental equations of motion.
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Your solution:
v0 vf dt
vAve and dv
a
\ l /
ds
Confidence Assessment: 3
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Given Solution:
Student Solution:
v0 and vf give you `dv = vf - v0 and vAve = (vf + v0) / 2.
`dv is divided by `dt to give accel. So we have a = (vf - v0) / `dt.
Rearranging this we have a `dt = vf - v0, which rearranges again to give vf = v0 + a `dt.
This is the second equation of motion.
vAve is multiplied by `dt to give `ds. So we have `ds = (vf + v0) / 2 * `dt.
This is the first equation of motion
Acceleration is found by dividing the change in velocity by the change in time. v0 is the starting velocity, if it is from rest it is 0. Change in time is the ending beginning time subtracted by the ending time. **
Question: **** Explain in detail how the flow diagram for the situation in which v0, a and `dt are known gives us the third fundamental equations of motion.
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Your solution:
vo a dt
\ \ /
dv
\ /
vf
\ / /
\ / /
dv
\ /
ds
Confidence Assessment:
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Given Solution:
a and `dt give you `dv. `dv and v0 give you vf. v0 and vf give you vAve. vAve and `dt give you `ds.
In symbols, `dv = a `dt.
Then vf = v0 + `dv = v0 + a `dt.
Then vAve = (vf + v0)/2 = (v0 + (v0 + a `dt)) / 2) = v0 + 1/2 a `dt.
Then `ds = vAve * `dt = [ v0 `dt + 1/2 a `dt ] * `dt = v0 `dt + 1/2 a `dt^2. **
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Self-critique (if necessary):
Self-critique Rating:3
Question: **** Why do we think in terms of seven fundamental quantities while we model uniformly accelerated motion in terms of five?
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Your solution: To understand uniformly accel. motion, you have to know all 7 quantities. The 5 most common are Vo, vf, a, dt and ds. You have to use these quantities to find the other two vAve and dv.
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Given Solution:
ONE WAY OF PUTTING IT:
The four equations are expressed in terms of five fundamental quantities, v0, vf, a, `dt and `ds. However to think in terms of meanings we have to be able to think not only in terms of these quantities but also in terms of average velocity vAve and change in velocity `dv, which aren't among these five quantities. Without the ideas of average velocity and change in velocity we might be able to use the equations and get some correct answers but we'll never understand motion.
ANOTHER WAY:
The four equations of unif accelerated motion are expressed in terms of five fundamental quantities, v0, vf, a, `dt and `ds.
The idea here is that to intuitively understand uniformly accelerated motion, we must often think in terms of average velocity vAve and change in velocity `dv as well as the five quantities involved in the four fundamental equations.
one important point is that we can use the five quantities without any real conceptual understanding; to reason things out rather than plugging just numbers into equations we need the concepts of average velocity and change in velocity, which also help us make sense of the equations. **
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Self-critique (if necessary):i understand this problem
Self-critique Rating:3
Question: **** Accelerating down an incline through a given distance vs. accelerating for a given time
Confidence Assessment: 3
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Given Solution:
If we accelerate down a constant incline our rate of change of velocity is the same whatever our initial velocity.
So the change in velocity is determined only by how long we spend coasting on the incline. Greater `dt, greater `dv.
If you travel the same distance but start with a greater speed there is less time for the acceleration to have its effect and therefore the change in velocity will be less.
You might also think back to that introductory problem set about the car on the incline and the lamppost. Greater initial velocity results in greater average velocity and hence less time on the incline, which gives less time for the car to accelerate. **
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Self-critique (if necessary):
i understand this problem after explaination.
Self-critique Rating:3
&#Good work. See my notes and let me know if you have questions. &#