General Questions: Motion in One Dimension

[courtrigrad]

1. Can you think of physical phenomena involving the Earth in which the Earth cannot be treated as a particle?
I would say the rotation of the earth. Would there be anything else? A particle is something in which rotational and vibrational considerations are disregarded. What would be a vibrational consideration?
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2. Average speed can mean the magnitude of the average velocity vector. Another meaning given to it is that average speed is the total length of path traveled divided by the elapsed time. Are these meanings different? If so, give an example.

So the average velocity vector is $\overline v = \frac{\Delta r}{\Delta t}$ where $\Delta r$ is a displacement vector. So the magnitude of this vector disregards the direction. I am guessing that these meanings are different because of the words length and displacement . Any ideas?

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3. When the velocity is constant, does the average velocity over any time interval differ from the instantaneous velocity at any instant?

I am guessing yes…because it depends on the length of the time interval. The velocity will be the same for all points, but the average velocity will be different (but constant). Is this correct?
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4. Is the average velocity of a particle moving along the x-axis $\frac{1}{2}(v_{x}_{0} + v_{x})$ when the acceleration is not uniform?

I am guessing that the average velocity is not equal to the above expression because the curve of $v_{x}$ versus $t$ would not be a line. Is this correct?
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5. Does the speedometer on an automobile register speed as we defined it?
Speed is the absolute value of instantaneous velocity, or $|\frac{dr}{dt}|$. So a speedometer doesn’t give the magnitude of the instantaneous velocity, it just gives ‘speed’ in miles per hour. Is this correct?
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6. (a) Can a body have zero velocity and still be accelerating? (b) Can a body have a constant speed and still have a varying velocity? (c) Can a body have a constant velocity and still have varying speed?

(a) I think a body can still be accelerating if it has zero velocity, because the velocity can still go up.
(b) Yes, because velocity has both direction and magnitude. So a body can have varying direction.
(c) No, because constant velocity assumes both a constant magnitude and direction.

Is this correct?
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7. Can an object have an eastward velocity while experiencing a westward acceleration?

I am guessing that it cannot, because the acceleration vector is basically the slope of the velocity vector. So they have to point in the same direction. Is this correct?

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8. Can the direction of the velocity change when its acceleration is constant?

I am guessing yes, because direction does not directly affect magnitude? Is this correct?
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9. If a particle is released from rest ($v_{y}_{o} = 0$) at $y_{o} = 0$ at the time $t = 0$. The equation for constant acceleration says that it is at position y at two different times, namely $\sqrt{\frac{2y}{a_{y}}}$ and $-\sqrt{\frac{2y}{a_{y}}}$. What is the meaning of the negative root in this equation?

This negative root is for positions that are negative (i.e. below the x-axis). Also how do they get these roots? IS it from the equation $v_{y}^{2} = v_{y}_{o}^{2} + 2a_{y}y$?
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10. What happens to our kinematic equations under the operation of time reversal, that is, replacing $t$ by -$t$?

I am guessing that the objects would move the opposite way to our reference frame. Is this correct?
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11. If a ball is thrown up, and air resistance is taken into account, would the time the ball rises be longer or shorter than the time during which it falls?

Intuitively, I would say it would take longer for the ball to go up. But could it be the same time? Or even shorter?
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12. Can there be motion in two dimensions when there is acceleration in one dimension?

Yes because an object can move up at a constant rate, while accelerating along the x-axis. Not really sure about this one.

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13. A man standing on the edge of a cliff at some height about the ground below throws one ball straight up with initial speed u and throws another ball straight down with the same initial speed. Which ball, if either, has the larger speed when it hits the ground? Neglect air resistance.

I would say the one being thrown up because it is at a larger distance above the ground, thus its speed increased quadratically. IS this correct?
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14. What are the dimensions of an angle? Can a quantity have units without having dimension?

I am guessing the dimensions of an angle are circular distance traveled divided by time. I think a quantity has to have both a unit and dimension (i.e. scalar). Is this correct?




Thanks a lot for any feedback. I know this is long, but please bear with me.

 

[Nenad]

1. Can you think of physical phenomena involving the Earth in which the Earth cannot be treated as a particle?
I would say the rotation of the earth. Would there be anything else? A particle is something in which rotational and vibrational considerations are disregarded. What would be a vibrational consideration?
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Thats a lot of questions to answer, General Relarivity and when dealing with gravity, the Earth cannot be taken as a particle.

2. Average speed can mean the magnitude of the average velocity vector. Another meaning given to it is that average speed is the total length of path traveled divided by the elapsed time. Are these meanings different? If so, give an example.

Your first statement is incorrect, velocity is displacement over time, your second statement is correct, average velocity is not related to average speed.

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3. When the velocity is constant, does the average velocity over any time interval differ from the instantaneous velocity at any instant?

I am guessing yes…because it depends on the length of the time interval. The velocity will be the same for all points, but the average velocity will be different (but constant). Is this correct?.

Correct

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4. Is the average velocity of a particle moving along the x-axis $\frac{1}{2}(v_{x}_{0} + v_{x})$ when the acceleration is not uniform?

I am guessing that the average velocity is not equal to the above expression because the curve of $v_{x}$ versus $t$ would not be a line. Is this correct?

This is correct, you would have a curve for your velocity vs. time graph.

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5. Does the speedometer on an automobile register speed as we defined it?
Speed is the absolute value of instantaneous velocity, or $|\frac{dr}{dt}|$. So a speedometer doesn’t give the magnitude of the instantaneous velocity, it just gives ‘speed’ in miles per hour. Is this correct??

A speedometer measures the distance traveled by the car in an amount of time, not velocity, so your assumption is correct.

6. (a) Can a body have zero velocity and still be accelerating? (b) Can a body have a constant speed and still have a varying velocity? (c) Can a body have a constant velocity and still have varying speed?

(a) I think a body can still be accelerating if it has zero velocity, because the velocity can still go up.
(b) Yes, because velocity has both direction and magnitude. So a body can have varying direction.
(c) No, because constant velocity assumes both a constant magnitude and direction.

Is this correct?

a) Throw a ball in the air, the moment it stops at the top, it has 0 velocity, but it is still acceleration downwards.
b) correct
c) If a car goes in an oval trac, it can vary its speed many times, but its velocity on the overall time intervall will be 0 since its displacement is 0.

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7. Can an object have an eastward velocity while experiencing a westward acceleration?

I am guessing that it cannot, because the acceleration vector is basically the slope of the velocity vector. So they have to point in the same direction. Is this correct?

Yes it can, like I said earlier, throw a ball in the air, initially, its velocity is upwards, but its acceleration is downeards.

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8. Can the direction of the velocity change when its acceleration is constant?

I am guessing yes, because direction does not directly affect magnitude? Is this correct?

Yes, gravity is one example.

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9. If a particle is released from rest ($v_{y}_{o} = 0$) at $y_{o} = 0$ at the time $t = 0$. The equation for constant acceleration says that it is at position y at two different times, namely $\sqrt{\frac{2y}{a_{y}}}$ and $-\sqrt{\frac{2y}{a_{y}}}$. What is the meaning of the negative root in this equation?

This negative root is for positions that are negative (i.e. below the x-axis). Also how do they get these roots? IS it from the equation $v_{y}^{2} = v_{y}_{o}^{2} + 2a_{y}y$?

solve the quadratic for time in the equation $$d = v_{0}t + \frac{1}{2}at^2$$?

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10. What happens to our kinematic equations under the operation of time reversal, that is, replacing $t$ by -$t$?

I am guessing that the objects would move the opposite way to our reference frame. Is this correct?

Ill let you think about this one.

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11. If a ball is thrown up, and air resistance is taken into account, would the time the ball rises be longer or shorter than the time during which it falls?

Intuitively, I would say it would take longer for the ball to go up. But could it be the same time? Or even shorter?

It takes longer for the ball to come down than to go up. Air resistance decreases the balls gravitational potential, resultiong in a smaller speed than initial speed. Draw the situation out with two particles, youll see what I mean.

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12. Can there be motion in two dimensions when there is acceleration in one dimension?

Yes because an object can move up at a constant rate, while accelerating along the x-axis. Not really sure about this one.

Yes, projectiles do this every day, gravity acts ony in the y-axis while the x-axis has a constant velocity.

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13. A man standing on the edge of a cliff at some height about the ground below throws one ball straight up with initial speed u and throws another ball straight down with the same initial speed. Which ball, if either, has the larger speed when it hits the ground? Neglect air resistance.

I would say the one being thrown up because it is at a larger distance above the ground, thus its speed increased quadratically. IS this correct?
.

No, they will both have the same speed on impact, since when the ball thrown up comes back to the throwers level, it will have the same initial velocity, but in the opposite direction, just like the ball being thrown down.

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14. What are the dimensions of an angle? Can a quantity have units without having dimension?

I am guessing the dimensions of an angle are circular distance traveled divided by time. I think a quantity has to have both a unit and dimension (i.e. scalar). Is this correct?.

It has no units. An angle, is the arc length divided by the radius of curvature.


I hope I have been of some help.

Regards,

Nenad

 

[courtrigrad]

Your first statement is incorrect, velocity is displacement over time, your second statement is correct, average velocity is not related to average speed.

Isn't that what I said?

10. What happens to our kinematic equations under the operation of time reversal, that is, replacing $t$ by - $t$?

I am guessing that the objects would move the opposite way to our reference frame. Is this correct?

I think the equations would have no practical meaning. Is this correct?

Thanks

 

[HallsofIvy]

Tides are a phenomenon that certainly would not make sense thinking of the Earth as a point mass (which is what I believe you mean by "particle").

 

[Nenad]

Isn't that what I said?

No its not what you said, you can have an average speed of any number while having the average velocity be 0. Imagine a car traveling in an oval course, the displacement is 0, but the distance traveled is the length of the track. Now tell me, is the magnitude of the average velocity equal to the average speed?.

Regards,

Nenad