The location of the point with lowest kinetic energy

[songoku]

Homework Statement

On the tables, we located two points, P1 and P2. A particle moves from P1 to P2 without acceleration along five different paths. The duration is the same for all paths. If we put a point X, the suitable path with the lowest kinetic energy is
a. A
b. B
c. C
d. D
e. E

Relevant Equations

Not sure

I am not sure I understand the question. I imagine there is a horizontal table and all the diagrams are the top-view of the table.

The question states that "A particle moves from P1 to P2 without acceleration along five different paths". In the first picture, I think the path is in the shape of oval and the particle does not pass through point P1. And I also don't understand how can the particle moves in the path given by picture (a), (b), (c) and (d) without acceleration (constant velocity)

At first I thought the answer will be (c) because I imagine it moves just like in simple harmonic motion and point X is at its amplitude so zero velocity but considering "without acceleration", I do not know anymore.

Thanks

 

[Lnewqban]

Can you show us the equation for kinetic energy?
Can you show us the equation for acceleration?
Can you show us the equation for velocity?
What non-accelerated motion means?

Path A is confusing, since location of P1 seems to be off the path.

 

[Halc]

The question states that "A particle moves from P1 to P2 without acceleration along five different paths". In the first picture, I think the path is in the shape of oval and the particle does not pass through point P1. And I also don't understand how can the particle moves in the path given by picture (a), (b), (c) and (d) without acceleration (constant velocity)

I noticed both those things, and you're right about them. First picture thus seems unqualified.
I can guess that they mean the particle maintains constant speed (not constant velocity) as it traverses each respective path, in which case the task is simply to identify the shortest path, which requires the lowest speed and thus minimum KE.
Where they put 'point X' seems irrelevant.

2nd guess: The problem is testing your knowledge of 'without acceleration'.
They already have an invalid figure that doesn't meet the criteria (P1 not being on path), so maybe only one of them meets the criteria and all the other ones violate the description since they require acceleration. You're meant to choose the only one that meets the problem description.

Both guesses yield the same answer. I thought it asked for max KE at first.

 

[Delta2]

I think the problem should have stated "without tangential acceleration", because there is no way to do a curved path motion without having at least normal acceleration.
But then again I don't understand what is the role of point X, if there is no tangential acceleration, kinetic energy remains the same through the whole path so its the same for all points (of a given curved path). Badly worded problem for sure.

 

[songoku]

Can you show us the equation for kinetic energy?

$KE = \frac {1}{2} m v^2$

Can you show us the equation for acceleration?

Change in velocity over time

Can you show us the equation for velocity?

Not sure about this one. Maybe integration of acceleration with respect to time

What non-accelerated motion means?

Motion where the velocity is constant

I noticed both those things, and you're right about them. First picture thus seems unqualified.
I can guess that they mean the particle maintains constant speed (not constant velocity) as it traverses each respective path, in which case the task is simply to identify the shortest path, which requires the lowest speed and thus minimum KE.
Where they put 'point X' seems irrelevant.

2nd guess: The problem is testing your knowledge of 'without acceleration'.
They already have an invalid figure that doesn't meet the criteria (P1 not being on path), so maybe only one of them meets the criteria and all the other ones violate the description since they require acceleration. You're meant to choose the only one that meets the problem description.

Both guesses yield the same answer. I thought it asked for max KE at first.

With all the assumptions the answer will be (e)

I think the problem should have stated "without tangential acceleration", because there is no way to do a curved path motion without having at least normal acceleration.
But then again I don't understand what is the role of point X, if there is no tangential acceleration, kinetic energy remains the same through the whole path so its the same for all points (of a given curved path). Badly worded problem for sure.

Yes I am also confused what the point X is for when the question asks about path

 

[Lnewqban]

$KE = \frac {1}{2} m v^2$

Change in velocity over time

Not sure about this one. Maybe integration of acceleration with respect to time

Motion where the velocity is constant

Please, excuse me for asking you all those questions; I was not sure how familiar you were with these concepts.
Yes, the problem is very confusing and the answer can be very simple.

The equation of energy tells us that the path that allows the smaller value of velocity is the answer.
The problem should have referred to speed rather than velocity, because speed is a scalar quantity and does not keep track of direction while velocity is a vector quantity and is direction dependent.

Since there is no acceleration (as a scalar, I assume) along each path, there is no change of the value of the speed.
Speed depends on the traveled distance and on the inverse of the time it takes for the particle to move from P1 to P2.

Since the duration of travel is the same for each path, time is the same for all, leaving us with the smallest traveled distance as the one that consumes or demands less energy from the particle.

 

[songoku]

Thank very much for all the help and explanation Lnewqban, Halc, Delta2

 

[Lnewqban]

You are welcome, songoku
Hopefully, the right response is as easy to reach as we have discussed.
Best

 

[shivaprasadvh]

Homework Statement:: On the tables, we located two points, P1 and P2. A particle moves from P1 to P2 without acceleration along five different paths. The duration is the same for all paths. If we put a point X, the suitable path with the lowest kinetic energy is
a. A
b. B
c. C
d. D
e. E
Relevant Equations:: Not sure

View attachment 264943
I am not sure I understand the question. I imagine there is a horizontal table and all the diagrams are the top-view of the table.

The question states that "A particle moves from P1 to P2 without acceleration along five different paths". In the first picture, I think the path is in the shape of oval and the particle does not pass through point P1. And I also don't understand how can the particle moves in the path given by picture (a), (b), (c) and (d) without acceleration (constant velocity)

At first I thought the answer will be (c) because I imagine it moves just like in simple harmonic motion and point X is at its amplitude so zero velocity but considering "without acceleration", I do not know anymore.

Thanks

Option is E.
Here when an object moves from point p1 to p2 in same time say x seconds and zero acceleration. To cover from p1 to p2 point, with minimum velocity in x seconds should have a shortest path. This should be a straight line. Hence E.

 

[haruspex]

Option is E.
Here when an object moves from point p1 to p2 in same time say x seconds and zero acceleration. To cover from p1 to p2 point, with minimum velocity in x seconds should have a shortest path. This should be a straight line. Hence E.

As indicated in post #6.