query 7 

course phy 201

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assignment #007

007. `query 7

Physics I

02-18-2008

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00:10:25

Describe the flow diagram you would use for the uniform acceleration situation in which you are given v0, vf, and `dt.

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RESPONSE -->

v0,vf,'dt

('dt)---------------'ds ( v0)

! \ / / /

! \ / / /

! vAve / /

! \ / /

! \ / /

! ( vf ) /

! \ /

! \ /

a-------------------------'dv

where () is given

confidence assessment: 3

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00:11:27

** We start with v0, vf and `dt on the first line of the diagram.

We use vO 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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RESPONSE -->

i believe mine is in a bit of a different shape but i want to think it still looks the same

self critique assessment: 1

The given quantities are v0, vf and `dt. Your diagram appears to assume v0, `dt and `ds.

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00:17:32

Describe the flow diagram you would use for the uniform acceleration situation in which you are given `dt, a, v0

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RESPONSE -->

'dt a v0

ok im going to try this in a different way

since you can use v0+a *'dt to find vf then i am going to say on the first line v0connected to a diagonally with a connected to 'dt straight lined across. which leads us to vf through a line to v0.

confidence assessment: 2

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00:18:07

** Student Solution: Using 'dt and a, find 'dv.

Using 'dv and v0, find vf.

Using vf and vO, find vave.

Using 'dt and Vave, find 'ds. **

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RESPONSE -->

ok so i may have used the wrong equation

self critique assessment: 1

You used vf = v0+a *'dt.

If you follow the reasoning used in the given you see the meaning of your equation.

Using 'dt and a, find 'dv. (the result is `dv = a `dt, which follows from the definition of acceleration)

Using 'dv and v0, find vf. (from the meaning of `dv we see that vf = v0 + `dv; since `dv = a `dt this gives us vf = v0 + a `dt)

Using vf and vO, find vave. (from v0 and vf we find vAve = (v0 + vf) / 2; if we substitute vf = v0 + a `dt into this expression we have vAve = v0 + 1/2 a `dt)

Using 'dt and Vave, find 'ds. (multiply vAve by `dt; according to the preceding result `ds vAve `dt = (v0 + 1/2 a `dt) `dt = v0 `dt + 1/2 a `dt^2, which is the third equation of motion).

This line of reasoning is the justification for the third equation of motion and reveals the meaning and the origin of that equation. This exercise in reasoning is completely grounded on the definitions of velocity and acceleration.

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00:20:36

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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RESPONSE -->

v0, vf, 'dt

o i know this one

since you can use the equation vf=v0+a'dt

then you know that if you divide both sides by 'dt and then subtract both sides of v0 you will be left with a where all lines ends

confidence assessment: 3

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00:23:24

**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. **

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RESPONSE -->

ARG !!!!

ok i used the wrong equation again. BUT, cant my way work too cause im just isolating the a in an equation that is a bit different .

self critique assessment: 1

You described a very good and correct solution using the equation.

However direct reasoning is based on more fundamental concepts than the equations, and it's important to understand the steps in the reasoning.

It's equally important to be able to use the equations, and you are doing really well with that aspect.

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00:24:53

qaExplain 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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RESPONSE -->

v0,a,'dt

im afraid to tell you the first thing that comes to mind cause it is probally wrong.

but here goes

'ds can be found by v0'dt+.5a'dt^2

self critique assessment: 1

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00:25:33

** 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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RESPONSE -->

sorta

self critique assessment: 1

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00:28:23

Why do we think in terms of seven fundamental quantities while we model uniformly accelerated motion in terms of five?

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RESPONSE -->

i would love to tell you why but i can only come up with 6 so im not sure

uni acc mot = vf, vo, a, 'dt, 'ds

fund = vf, vo, a, 'dt, 'ds, vAve

unless its aAve

basically we break down the other not mentioned forms into their compoenets and with the over lap they are no longer needed

confidence assessment: 0

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00:29:32

** 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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RESPONSE -->

crap it was change of

self critique assessment: 1

your response was cut off but I think you were about to say something about `dv.

Remember that everything starts from the definitions, which give us

vAve = `ds / `dt and

aAve = `dv / `dt.

Those two definition contain five of the seven quantities in terms of which we think about uniformly accelerated motion on an interval.

It's natural to also think in terms of v0 and vf.

In fact since, for uniformly accelerated motion, vAve = (v0 + vf) / 2 (this is a consequence of the linearity of the v vs. t graph when acceleration is uniform), and since `dv = vf - v0, we can reformulate the two definitions

vAve = `ds / `dt and

aAve = `dv / `dt

to give us

(vf + v0) / 2 = `ds / `dt and

a = (vf - v0) / `dt.

Solving the first equation for `ds gives us the first equation of motion, and solving the second for vf gives us the second.

Eliminating vf between the first and second equation gives us the third; eliminating `dt between the first and second gives us the fourth.

The four equations of motion are a direct result of the definitions of velocity and acceleration, and it's important to understand how all seven of the quantities v0, vf, `dt, `ds, a, vAve and `dv occur in any given problem, and how these variables are related. It is equally important to be able to use the four equations of motion to solve a problem.

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00:37:10

Accelerating down an incline through a given distance vs. accelerating for a given time

Why does a given change in initial velocity result in the same change in final velocity when we accelerated down a constant incline for the same time, but not when we accelerated down the same incline for a constant distance?

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RESPONSE -->

because when measuring time you could change distance due to many factors friction, slope, terrain, ect.

when measuring distantce you have the smae considerations but you arent fixing your data based on stopping it at a certain time rather a point on the experiment

confidence assessment: 0

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00:37:51

** 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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RESPONSE -->

ok

self critique assessment: 3

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Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the given solution, and if necessary asking specific questions (to which I will respond).

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assignment #007

007. `query 7

Physics I

02-18-2008

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Your work looks good. See my notes. Let me know if you have any questions. &#