PHY 201
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For each situation state which of the five quantities v0, vf, `ds, `dt and a are given, and give the value of each.
• A ball accelerates uniformly from 10 cm/s to 20 cm/s while traveling 45 cm.
answer/question/discussion: ->->->->->->->->->->->-> :
The situation has v0, vf, and ‘ds. The initial velocity is 10 cm/s, the final velocity is 20cm/s, and change in position is 45 cm.
First I am going to find the vAve from the v0 and vf: (10 cm/s + 20 cm/s) / 2 = 15 cm/s. Then if you have the average velocity and the displacement, then you could get the change in time: ‘dt = ‘ds / vAve = 45 cm / 15 cm/s = 3 seconds.
Next, you the need the find the ‘dv which is 20 cm/s – 10 cm/s = 10 cm/s. Then you have the two variables to obtain a, which is ‘dv divided by the ‘dt, which is: 10 cm/s / 3 s = 3.33 cm/s/s.
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• A ball accelerates uniformly at 10 cm/s^2 for 3 seconds, and at the end of this interval is moving at 50 cm/s.
answer/question/discussion: ->->->->->->->->->->->-> :
I have been given the acceleration 10 cm/s/s, the time interval 3 seconds, and the final velocity 50 cm/s. So, I need to solve for the remaining variables.
First, if I know the time interval and the acceleration, then I could get the change in velocity: ‘dv = a * ‘dt = 10 cm/s/s * 3 s = 30 cm/s. So, if the change in velocity is 30 cm/s and the final velocity is 50 cm/s, then the initial velocity has to be 20 cm/s: 50 cm/s – 30 cm/s = 20 cm/s.
Next, you find the vAve when getting the averages of the initial and final velocities, which is: (20 + 50) / 2 = 35 cm/s. So, all there is left is the change in position, which is the average velocity multiplied by the time interval: 35 cm/s * 3 s = 105 cm.
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• A ball travels 30 cm along an incline, starting from rest, while accelerating at 20 cm/s^2.
answer/question/discussion: ->->->->->->->->->->->-> :
I am given the displacement 30 cm, the initial velocity 0 cm/s, and the acceleration 20 cm/s/s.
I am not sure how to get the rest of the variables with the three variables provided here, because they are directly related.
For this case you can't use direct reasoning, and it is to your credit that you realized this.
You would need to use the equations of uniformly accelerated motion to solve this problem. I usually suggest using the fourth equation to find the final velocity. Once you have that, you can reason out the rest.
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Then for each situation answer the following:
• Is it possible from this information to directly determine vAve?
answer/question/discussion: ->->->->->->->->->->->-> :
Yes, the first situation you can determine the vAve with the information given.
The second situation, however, you cannot find the average velocity, because you are not given the initial velocity.
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• Is it possible to directly determine `dv?
answer/question/discussion: ->->->->->->->->->->->-> :
Yes, for the first situation you can determine the change in velocity because you have the initial and final velocities.
The second situation, you can find the change in velocity, because you have the time interval and the acceleration, but you have to switch the equation around to solve for the change in velocity.
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45 minutes
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Excellent work on this one. See my one note and check out the link, just to reinforce the insights you have expressed here.
&#See any notes I might have inserted into your document. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#