Kinematics and displacement, who is right?

[jebat]

Hi everyone

I have an issue with my physics teacher about a question on displacement. I have inserted the screenshot of the question below. By the definition of displacement, I was sure, and still am sure my answer is correct. But my physics teacher insisted that I am wrong. Please, can anyone help me explain who is right? I have also inserted my argument that supports my conclusion. Thank you.

My solution:

 

[Mark44]

Summary:: Kinematics, Displacement

Hi everyone

I have an issue with my physics teacher about a question on displacement. I have inserted the screenshot of the question below. By the definition of displacement, I was sure, and still am sure my answer is correct. But my physics teacher insisted that I am wrong. Please, can anyone help me explain who is right? I have also inserted my argument that supports my conclusion. Thank you.

View attachment 256122

My solution:
View attachment 256123

IMO, the question could be worded better if "position" was asked for rather than "displacement." Displacement implies a movement from one point to another, at least the way I think of it.
In the figure, the initial position is negative, and the velocity is positive.

 

[Dr_Nate]

Summary:: Kinematics, Displacement

Hi everyone

I have an issue with my physics teacher about a question on displacement. I have inserted the screenshot of the question below. By the definition of displacement, I was sure, and still am sure my answer is correct. But my physics teacher insisted that I am wrong. Please, can anyone help me explain who is right? I have also inserted my argument that supports my conclusion. Thank you.

View attachment 256122

My solution:
View attachment 256123

You are correct and your reasoning is correct. Does your teacher even know the equation for average velocity?

 

[PeroK]

IMO, the question could be worded better if "position" was asked for rather than "displacement." Displacement implies a movement from one point to another, at least the way I think of it.
In the figure, the initial position is negative, and the velocity is positive.

It should ask for the initial displacement from the origin. The displacement changes with time; and displacement is generally relative to some point.

 

[Dr_Nate]

It should ask for the initial displacement from the origin. The displacement changes with time; and displacement is generally relative to some point.

Oh I see now. The origin is not the origin of some arbitrary coordinate system as we typically use it. It is literally the origin of the car, because he uses “its” and not “an”. Technically, your teacher is correct. But why play silly word games like that?

 

[PeroK]

Oh I see now. The origin is not the origin of some arbitrary coordinate system as we typically use it. It is literally the origin of the car, because he uses “its” and not “an”. Technically, your teacher is correct. But why play silly word games like that?

The teacher has interpreted "displacement" as initial displacement from the origin. The OP has interpreted "displacement" as "the displacement over time from the starting position of the car".

PS just to add that I would interpret "position" as a point in space, independent of coordinates. Once you choose your coordinates, then the initial position of the car is either at the origin or displaced from the origin, as it is in this case.

 

[Dale]

Summary:: Kinematics, Displacement

By the definition of displacement, I was sure, and still am sure my answer is correct. But my physics teacher insisted that I am wrong. Please, can anyone help me explain who is right?

Assuming that you want good marks then simply learn to provide the answer that the teacher is looking for and don’t worry about who is “right”.

In this case, the teacher intends “displacement” to mean “vector from the origin” while you intend “displacement” to mean “vector from the original location”. Both meanings are acceptable, so I would not present it as “right” or “wrong”. I would just tell the teacher that the question was ambiguous.

However, be aware that this could backfire. If in the lecture the professor said something like “in this class ‘displacement’ refers to the vector from the origin” then your complaint of ambiguity will indicate that you were not paying attention.

 

[vanhees71]

Hm, maybe it's a wise advice to just answer the question "that the teacher is looking for". This I was used to at high school in the non-science subjects only. If you wanted to get good marks in "Sozialkunde" (the high-school subject related roughly to what would be called sociology at university), you better argued according to the political opinion the teacher held (with the bizarre result that I answered the same question completely differently depending on which teacher asked it).

On the other hand, that's not reflecting the standards in the exact sciences. There only the observed facts count and how they are adequately described mathematically. Already the question is formulated in a way which does not hold the standards of a precise description. At least the arrow is missing indicating in which direction the basis vector is pointing along the street in this (admittedly one-dimensional) problem. Then "displacement" is not a common notion in physics. I'd have interpreted the text as the OP, because "displacement" should, as far as I understand English, which is not my mother tongue though, should mean the change of position of the car with time, and since the velocity points to the right (fortunately here the teacher indicated the velocity with its direction) and it was said to "take right as positive". That's why the answer is +,+ is correct. Since in the so understood reference frame $\vec{v}=v \vec{e}_x$ with $v>0$ also the displacement $\vec{x}-\vec{x}_0=\vec{v} t$ is also positive (for all $t>0$). If "displacement" is meant as the component of the position vector, $x$ it's of course, in the situation drawn in the figure, negative. Then "-,+" would be the correct answer, but the question is so sloppily formulated that you cannot answer it without explicitly writing what you understand by the vaguely formulated question.

In the exact sciences authority is not a valid argument, but of course, if the teacher doesn't accept to be possibly wrong and the student right, it's better not to argue to get good grades. The problem is that teachers who are used to such sloppy expressions of the science they should teach are usually not easy to convince to have made a mistake :-(.

 

[ZapperZ]

I agree that this is an issue of "displacement" being meant to be "position". Displacement is the change in position.

BTW, be careful that Δx is often defined as x_f - x_i. It looks like in the OP's explanation, he/she did x_i - x_f.

The way you argue this with your instructor is to look at the text. How was the word "displacement" defined? Are there examples, which there should be because doing this problem should not be the first time you have encountered the term "displacement"? Find an example (or more) that are consistent with the definition that displacement is the change in position.

Only then can you approach your instructor and present it to him/her your argument.

Zz.

 

[Cutter Ketch]

I will add to the growing litany of support. Displacement is final position - initial position. In this case the most reasonable interpretation is that the displacement is purely to the right = positive as you rightly argue. The fact that the question says “it’s origin” is bad english : unclear antecedent, the car’s origin or the road’s origin? This can be interpreted to mean the car’s origin, and the displacement would then be as your teacher suggests. However, that would imply some earlier time before the problem begins when the car originally started off at that zero point. That interpretation is patently ridiculous. You would be required to assume something that isn’t stated in the problem. That would be nothing short of stupid. I can see why this is bugging you.

 

[Herman Trivilino]

The car is being displaced towards the right, and the question says to take that direction as the positive direction.

The position is negative, the displacement (defined as change in position) is positive.

 

[Dale]

The position is negative, the displacement (defined as change in position) is positive.

The question says that the origin is “its origin” meaning the place that the car started. So it’s change in position is indeed negative.

At most, the question is ambiguous and confusing, but I would be very hesitant to go into the professor asserting that it is wrong.

 

[256bits]

Since its a race car, the car could have been going around a track starting at the origin, and coming back to its origin. It's velocity is positive and its displacement is positive.

 

[vanhees71]

The question says that the origin is “its origin” meaning the place that the car started. So it’s change in position is indeed negative.

At most, the question is ambiguous and confusing, but I would be very hesitant to go into the professor asserting that it is wrong.

The change in position is $\Delta \vec{e}_x=v \Delta t \vec{e}_x$. Since $v>0$ the change in position (or more clearly the change of the component of the position vector with respect to the chosen basis) is positive.

 

[sophiecentaur]

Please, can anyone help me explain who is right? I have also inserted my argument that supports my conclusion.

"+;+" could never the the correct answer because it would imply that the car's [initial] displacement would depend on its actual velocity. How could that be?
If displacement were supposed to refer to motion from the 'position' at t=0 then surely the initial 'displacement' would be Zero,. That would be ridiculous because the option does not exist in the list of alternatives and it also implies that there would be something 'special' about starting at the origin (when t=0). Ignore all the extra discussions about equations of motion etc. etc.; they just add confusion. You should start with the data you are supplied with and deal with that first. The logic leading to the 'correct' answer should be would have to be the same for all possible starting positions (displacements) and velocities.

 

[Dale]

The change in position is $\Delta \vec{e}_x=v \Delta t \vec{e}_x$.

This is only true if $v$ is constant over $\Delta t$

 

[jbriggs444]

This is only true if $v$ is constant over $\Delta t$

Slightly more general than that. Assuming that the acceleration exists and is integrable, it only requires that the integral of the acceleration over the time interval $\Delta t$ comes to zero.

 

[vanhees71]

Well, yes then the question is so illposed that it cannot be objectively answered ;-)).

 

[Dale]

Or “the question is so confusingly worded that an international panel of physics experts could not come to a consensus on the correct answer.”

 

[Ibix]

Or “the question is so confusingly worded that an international panel of physics experts could not come to a consensus on the correct answer.”

I do not recommend this as an approach to a potentially grumpy professor, but I think it sums up the thread nicely.