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Debate with teacher about physics question

  1. Jun 14, 2015 #1
    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.
  2. jcsd
  3. Jun 14, 2015 #2
    Well, there is obviously a problem but answering such a question with D where you have the option C is not very logical.
  4. Jun 14, 2015 #3


    Staff: Mentor

    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.
  5. Jun 14, 2015 #4
    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)
  6. Jun 14, 2015 #5
    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.
  7. Jun 15, 2015 #6
    thank you, that's exactly what I meant. but you can see either the answer or question was wrong.
  8. Jun 15, 2015 #7


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    No, it could also move with constant velocity.

    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".
  9. Jun 15, 2015 #8
    What I meant here is what I have understood on the given question. :smile:

    I agree with this.
  10. Jun 15, 2015 #9


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    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.
  11. Jun 15, 2015 #10


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    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!
  12. Jun 15, 2015 #11
    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".
  13. Jun 15, 2015 #12
    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.

  14. Jun 15, 2015 #13
    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.
  15. Jun 15, 2015 #14
    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.
  16. Jun 15, 2015 #15
    No it isn't - the question didn't say anything about the velocity of the object.
  17. Jun 15, 2015 #16


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    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.
  18. Jun 15, 2015 #17
    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?
    Last edited: Jun 15, 2015
  19. Jun 15, 2015 #18


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    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​

    If the object has zero acceleration the object must be at rest
    A: True
    B: False​
  20. Jun 15, 2015 #19
    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.
  21. Jun 15, 2015 #20


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    "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.
  22. Jun 15, 2015 #21
    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...
  23. Jun 15, 2015 #22
    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.
  24. Jun 15, 2015 #23
    ... 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.
  25. Jun 16, 2015 #24
    But it could. Infact 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.

  26. Jun 16, 2015 #25
    Only if p is true.

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