Is Zero Acceleration Proof That an Object Must Be at Rest?

[sachaw]

In a recent exam, the question came up ""If the object has zero acceleration the object must be at rest" is this statement:
A: Always true
B: True in space
C: Sometimes true
D: Never true"
Obviously we can cross of the first two, but for the other two its not so easy, for this question I answered D- never true as it states that "the object MUST be at rest", if I understand the word "must" correctly it should mean that under no circumstances the object will move and be no longer at rest, I proceed to ask the teacher that wrote the question, from what he told me that the question was meant to ask whether an object with zero acceleration can be at rest, but due to the wording (replacing "can be" with "must") it changes the question completely, therefore changing the answer.

 

[TESL@]

Well, there is obviously a problem but answering such a question with D where you have the option C is not very logical.

 

[jedishrfu]

First an object with zero acceleration in your inertial frame will either be stationary or will be moving at a constant velocity.

Hence the sometimes true is the correct answer.

If you answered D then you've excluded the possibility of the object moving at a constant velocity in your inertial frame of reference.

 

[sachaw]

First an object with zero acceleration in your inertial frame will either be stationary or will be moving at a constant velocity.

Hence the sometimes true is the correct answer.

If you answered D then you've excluded the possibility of the object moving at a constant velocity in your inertial frame of reference.

I fully understand that concept, but if you read the second half of my message more closely I state that the question changes, rather than asking whether it can be at rest is asked weather it must be at rest, and and object does not necessarily have to be at rest (must)

 

[ecastro]

I think it goes like this:

If the object has zero acceleration, then it implies (automatically) that the object is at rest.

If we change the wording to "can be": "If the object has zero acceleration the object can be at rest". The answer to this question is A. Always true, because "can be" implies that the two possibilities of being at rest and not.

 

[sachaw]

I think it goes like this:

If the object has zero acceleration, then it implies (automatically) that the object is at rest.

If we change the wording to "can be": "If the object has zero acceleration the object can be at rest". The answer to this question is A. Always true, because "can be" implies that the two possibilities of being at rest and not.

thank you, that's exactly what I meant. but you can see either the answer or question was wrong.

 

[A.T.]

If the object has zero acceleration, then it implies (automatically) that the object is at rest.

No, it could also move with constant velocity.

If we change the wording to "can be": "If the object has zero acceleration the object can be at rest". The answer to this question is A. Always true, because "can be" implies that the two possibilities of being at rest and not.

Either way it would be linguistically unnecessarily complicated. If you have choices like "sometimes true", "always true" then the statement to be evaluated should just read "is at rest".

 

[ecastro]

No, it could also move with constant velocity.

What I meant here is what I have understood on the given question.

Either way it would be linguistically unnecessarily complicated. If you have choices like "sometimes true", "always true" then the statement to be evaluated should just read "is at rest".

I agree with this.

 

[Khashishi]

Your argument hinges on the inexact language used here, but frankly, c is a better answer, since you can conceivably add additional premises such that the statement becomes true.

 

[PeroK]

In a recent exam, the question came up ""If the object has zero acceleration the object must be at rest" is this statement:
A: Always true
B: True in space
C: Sometimes true
D: Never true"
Obviously we can cross of the first two, but for the other two its not so easy, for this question I answered D- never true as it states that "the object MUST be at rest", if I understand the word "must" correctly it should mean that under no circumstances the object will move and be no longer at rest, I proceed to ask the teacher that wrote the question, from what he told me that the question was meant to ask whether an object with zero acceleration can be at rest, but due to the wording (replacing "can be" with "must") it changes the question completely, therefore changing the answer.

I think you're logically correct, but it's clearly not what the questioner intended. You should stop thinking like that or give up physics and study logic and pure mathematics instead!

 

[DrStupid]

If you answered D then you've excluded the possibility of the object moving at a constant velocity in your inertial frame of reference.

No, that's what you exclude with answer C. "the object must be at rest" is equivalent with "the object cannot be in motion". Answer D means "the object can always be in motion".

 

[lightarrow]

In a recent exam, the question came up ""If the object has zero acceleration the object must be at rest" is this statement:
A: Always true
B: True in space
C: Sometimes true
D: Never true"
Obviously we can cross of the first two, but for the other two its not so easy, for this question I answered D- never true as it states that "the object MUST be at rest", if I understand the word "must" correctly it should mean that under no circumstances the object will move and be no longer at rest, I proceed to ask the teacher that wrote the question, from what he told me that the question was meant to ask whether an object with zero acceleration can be at rest, but due to the wording (replacing "can be" with "must") it changes the question completely, therefore changing the answer.

I understand your point of view because it's possible to interpret the question as you did. But let's make an example. If, referring to a specific problem, I say:
"we know that the object velocity is zero, so if the object has zero acceleration the object must be at rest"
is it a correct statement?
That's another way to interpret the question and in this case the right answer would be C.

--
lightarrow

 

[DrStupid]

"we know that the object velocity is zero, so if the object has zero acceleration the object must be at rest"
is it a correct statement?

The object would still be in motion in other frames of reference. From this point of view answer D would be correct again. It think we have a good example for a bad question.

 

[pbuk]

You are right, the teacher is (and some posters in this thread are) wrong.

Of course it is correct that the statements (A) "The object has zero acceleration" and (B) "the object [is] at rest" are sometimes both true, but that is not what the question says - the statement does not refer to a hypothetical single object which may be both non-accelerating and in motion, it refers to the set of all objects and makes a proposition which is always either true or false. The statement in the question says "If A [then] B", or A ⇒ B - and because we can easily find a counter example where A is true and B is false then A ⇒ B is clearly false: the word "always" is redundant here.

The question the examiner seems to have intended is "An object with zero acceleration is at rest" - and in some sense this statement is "sometimes true" - however this is a very unscientific use of the concept of truth. In fact the more I look at it the worse it gets - this is no way to teach science.

 

[pbuk]

"we know that the object velocity is zero, so if the object has zero acceleration the object must be at rest"
... That's another way to interpret the question

No it isn't - the question didn't say anything about the velocity of the object.

 

[cjl]

D is clearly the correct answer here, due to the use of the word "must". The statement "An object undergoing zero acceleration must be at rest" is always false. Now, if the statement were "An object undergoing zero acceleration is at rest", C would be the best answer, but given the presence of "must" in the statement, C is not correct.

 

[pbuk]

I think some people are being confused here (not cjl, our posts crossed) - let's use a slightly different question:

"If an object is rotating it must be on fire". Is this statement "sometimes true"? When?

 

[A.T.]

D is clearly the correct answer here, due to the use of the word "must".

Right. The clear way to pose the question the teacher actually wanted to ask would be:

If the object has zero acceleration the object is at rest

A: Always true
B: Never true
C: Sometimes true​

or:

If the object has zero acceleration the object must be at rest

A: True
B: False​

 

[pbuk]

If the object has zero acceleration the object is at rest

A: Always true
B: Never true
C: Sometimes true​

That is still not clear to me, you need the proposition to be "An object has zero acceleration and the object is at rest". THAT can sometimes be true.

 

[jbriggs444]

If the object has zero acceleration the object is at rest

A: Always true
B: Never true
C: Sometimes true​

That is still not clear to me, you need the proposition to be "An object has zero acceleration and the object is at rest". THAT can sometimes be true.

"An object has zero acceleration and the object is at rest" taken formally means "An object does not have zero acceleration OR the object is at rest".

i.e. "if p then q" means the same as "(not p) or q"

But that turns out to be irrelevant. There are four mathematical possibilities for p and q.

The object has zero acceleration and is at rest. (physically possible)
The object has zero acceleration and is not at rest (physically possible)
The object does not have zero acceleration but is at rest (physically possible -- that it is at least momentarily at rest).
The object does not have zero acceleration and is not at rest (physically possible)

Every non-trivial logical statement involving p and q will be sometimes true and sometimes false. So C is going to be the answer regardless of whether we use and's, or's, if's or not's.

 

[ModusPwnd]

I think you are right, this is a case of a poorly worded question. Its never true because its never the case that it "must" be at rest. The "must" shouldn't have been put in there. It adds nothing but confusion, in this case it confused your teacher. This happens more often than it should in class and tests...

 

[pbuk]

"An object has zero acceleration and the object is at rest" taken formally means "An object does not have zero acceleration OR the object is at rest".

I think you mean "If an object has zero acceleration then the object is at rest" taken formally means "An object does not have zero acceleration OR the object is at rest"., but that is not the statement that we have here, we have "If an object has zero acceleration then the object MUST BE at rest". The words MUST BE invalidate your translation from informal linguistic logic to formal propositional logic otherwise you admit linguistic absurdities such as in my post #17.

 

[pbuk]

... and if you admit that "If an object is rotating then it must be on fire" is meaningful, then you must admit "If an object is wobbly then it must be Tuesday".

The reason we get absurd statements like these is that the formal symbols ∧, ∨ and ~ which are read as "and", "or" and "not" have similar meanings as these words used in informal linguistic logic, however the formal symbol → which is read as "implies", or sometimes "if ... then" does NOT have an equivalent meaning to these words when used in language.

Consider: p = "It is raining"; q = "It is Tuesday". The expressions p ∧ q, p ∨ q and even p → q = (~p) ∨ q are all valid, and "It is raining and it is Tuesday", "(Either) it is raining or it is Tuesday" and even "Either it is not raining or it is Tuesday" all make sense (and their truth or falsity corresponds to the truth tables of the equivalent formal expressions), but "It is raining implies it is Tuesday" or "If it is raining then it is Tuesday" express absurdities.

 

[lightarrow]

No it isn't - the question didn't say anything about the velocity of the object.

But it could. In fact C answer is "sometimes" true.
The question talks about "the" object, not "an" object, so it can refer to a specific object in a specific situation and not to a general object in a general situation.

--
lightarrow

 

[DrStupid]

i.e. "if p then q" means the same as "(not p) or q"

Only if p is true.

The object has zero acceleration and is not at rest (physically possible)

That means p=true and q=false and therefore falsifies "if p then q".

 

[jbriggs444]

That means p=true and q=false and therefore falsifies "if p then q".

That's half of what could be a correct statement. The other half is that p=true and q=false also falsifies "(not p) or q".

Which means that this case is consistent with the claim that " 'if p then q' is equivalent to '(not p) or q' "

 

[DrStupid]

But it could.

For my taste "if A then B" is different from "if (A and C) then B".

 

[cjl]

But it could. In fact C answer is "sometimes" true.
The question talks about "the" object, not "an" object, so it can refer to a specific object in a specific situation and not to a general object in a general situation.

--
lightarrow

No, C is never true, due to the use of the word "must". Even if a particular object is stationary and unaccelerating, the fact that it is unaccelerating does not mean that it must be stationary, since it is also possible for that object to be moving and unaccelerating.

 

[Fredrik]

The obvious way to interpret the question is "If the object has zero acceleration the object must be at rest in the inertial coordinate system S". It's "sometimes true" in the sense that its truth value depends on S, just like how the truth value of the statement x=1 depends on the value of x.

Yes, the question is very badly worded, but I think it's still pretty obvious that the person who wrote the question intended C to be the correct answer.

 

[cjl]

No, it is false, in the same sense that stating "if y=x^2, must Y be equal to 1" is false. Yes, Y=1 is a possibility, given the constraints of the problem, but it isn't the only possibility, and thus the statement is false.

 

[gmax137]

I think some people are being confused here (not cjl, our posts crossed) - let's use a slightly different question:

"If an object is rotating it must be on fire". Is this statement "sometimes true"? When?

I'm really surprised there was any argument at all following this post.

 

[russ_watters]

Yes, the question is very badly worded, but I think it's still pretty obvious that the person who wrote the question intended C to be the correct answer.

To this I would add that if someone was aware enough of the issue to answer D, it would have been best to ask the teacher to clarify during the test.

 

[cjl]

To this I would add that if someone was aware enough of the issue to answer D, it would have been best to ask the teacher to clarify during the test.

I disagree. As worded, the answer is very clearly D, and I would not have hesitated (were I in that class) to answer as such. There's nothing about the question that needs clarification.

 

[russ_watters]

I disagree. As worded, the answer is very clearly D, and I would not have hesitated (were I in that class) to answer as such. There's nothing about the question that needs clarification.

The double, conflicting qualifiers are a poor wording choice regardless of the question's intent.

Edit: the "clarification" by the teacher ("can be" instead of "must") flips the problem over, but doesn't fix it. It should say "is".

 

[Fredrik]

No, it is false, in the same sense that stating "if y=x^2, must Y be equal to 1" is false. Yes, Y=1 is a possibility, given the constraints of the problem, but it isn't the only possibility, and thus the statement is false.

I assume that you meant to say "if y^2=1 then y=1". This is a sentence, but not a statement (=a sentence that's either true or false). You need a "for all" to turn it into a statement, and there's more than one option, for example:

(a) For all real numbers y, if y^2=1 then y=1.
(b) For all positive real numbers y, if y^2=1 then y=1.​

Statement (a) is false, but statement (b) is true. So you actually made a mistake that's very similar to the one made by the guy who wrote that question.

"If an object is rotating it must be on fire". Is this statement "sometimes true"? When?

When the scope of the "for all" that turns this sentence into a statement is a subset of the set of all objects that are on fire.

You could argue that my argument is irrelevant since I'm ignoring the intended meaning of the sentence, but those of you who argued that D is the only correct answer did that too, so if my argument is irrelevant, then so is yours.