Simple motion graphs i need some clarification

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The discussion focuses on understanding motion graphs and the effects of incline on velocity and acceleration. The participant shares their answers to a worksheet and seeks clarification on whether incline affects velocity, noting that A and F have the same motion but differ in direction. It is confirmed that while A and F have the same velocity, their accelerations differ due to the incline's impact on gravitational acceleration. Additionally, B and E maintain constant velocity with zero acceleration, while C is slowing down, indicating the lowest acceleration. The conversation concludes with reassurance that the participant is on the right track and encourages further thought on the topic.
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Ok. Please look at the attachment for the first part, and this web link for the second part. http://www.prenhall.com/divisions/esm/adv/tiponline/rankingtask/files/01KINEMA/kine003.pdf

For the first worksheet, this is what I have so far.
1. A
2. D
3. F
4. E
5. B
6. C
Is it right, or what do I need to change?

One question that I am unsure about is...does incline affect the velocity? A and F have the same motion, but one is going in the downward direction, and the other is going in the upward direction. But because their motion is the same, can I say that their velocity is the same also??

The second pdf file:

I said its going to be:
1. A
2. D
3. F
4. E
5. B
6. C

I know that B and E have constant velocity, so their acceleration is zero. C is slowing down, so its acceleration will be the lowest.
Now what I'm debating is that the motion of A, F, (maybe D) are the same, its just that their on different inclines. But does this mean their accelerations are the same also? Yea, I definitely need some clarification here.
 

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You're on the right track. Just give it some more thought.

You are thinking that the incline is significant because you know from experience that things usually accelerate downhill. Why is that so?

Now, in these problems, you are not told what force, if any, is acting on these balls. Is it gravity, electrostatic force, maybe wind ... ? Are they on the surface of the earth, or in deep space?

All you know are the various successive positions of the balls relative to their previous positions, and you are told that the time intervals are constant. (It is not stated, but I guess you can assume that the scale is the same in all of the drawings.) So you can assume that where the speed changes, there is acceleration, and where there is acceleration, there is SOME force.

So, what's faster, 60 mph uphill or 60 mph downhill?
 


First of all, great job on the first part of the worksheet! Your answers are correct. As for the question about incline affecting velocity, you are correct in saying that the motion is the same for both A and F, so their velocities should be the same as well. Inclination does not affect velocity, but it does affect the acceleration due to gravity. This means that the acceleration for A and F will be different, but their velocities will be the same.

For the second part of the worksheet, your answers are also correct. B and E have constant velocity, so their acceleration is zero. C is slowing down, so its acceleration will be the lowest. As for A, D, and F, their motion is the same, but their accelerations will be different due to the different inclines. This is because the acceleration due to gravity is affected by the angle of the incline.

I hope this clarifies your doubts. Keep up the good work!
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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