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Consider an object moving with an acceleration $a = -1 \text{m/s}^2$ starting with speed $v(0) = 4 \text{m/s}$ towards east and stopped after 4 seconds. (There are no friction.)

After 4 seconds, the object would have speed $v(4\text{s})=0$.

  • Question 1: Does the object get value of a null vector (0 vector) after it completely stops?

  • Question 2: Since the object was moving toward east and then stopped at 4 seconds, can it be said that the object changed directions when it stopped?

I mean, the direction changes : East -> None and The vector changes to a null vector too.

  • Question 3: The object stopped moving so it doesn't have a direction. So, is a change from east to none make a valid 'directional change'?

Sorry for the bad english..... it isn't my native language

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    $\begingroup$ The object is the object. A vector is a directional property of the object. Where the object's position and velocity vectors point and what length they have depends entirely on the observer's coordinate system. Two different observers can describe the object's movement with different position and velocity vectors and they would both be right. $\endgroup$
    – CuriousOne
    Commented Jul 6, 2015 at 6:29
  • $\begingroup$ @CuriousOne Could you tell me a bit more? The object stopped moving so it doesn't have a direction. So, is a change from east to none make a valid 'directional change'? $\endgroup$
    – juyoung518
    Commented Jul 6, 2015 at 6:31
  • $\begingroup$ Welcome to Physics Stack Exchange. Whenever you find yourself making a list of questions, please stop and instead post each question separately. The goal of this site is to produce clear and correct sets of specific questions and answers. Putting multiple questions in one post prevents this. Now to talk about the specific question: it's not at all clear what you mean by "Is the object a null vector". $\endgroup$
    – DanielSank
    Commented Jul 6, 2015 at 7:22
  • $\begingroup$ @DanielSank Sorry for my bad english... I mean that the object gets a value of null in vector (0vector) $\endgroup$
    – juyoung518
    Commented Jul 6, 2015 at 7:33
  • $\begingroup$ Apologizing is not necessary, and unfortunately it doesn't help us understand the question. Can you please explain (by editing your post) what you mean by "Is the object a null vector"? $\endgroup$
    – DanielSank
    Commented Jul 6, 2015 at 7:35

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I feel like you are asking more about language rather than about physics.

An important concept is velocity. Velocity is a vector that points in the direction of travel of the object and its magnitude is the speed of the object. In the following I assume you are talking about velocity whenever you talk about vectors in your question. In that case,

Question 1. The velocity will be (in, say, three dimensions) $\vec v=(0,0,0)$. That is probably what you mean by null vector.

Question 2. The issue here is that the velocity doesn't point in any direction (direction simply is not defined for a vector like (0,0,0)). You may or may not call the change {going east $\to$ going nowhere} a direction change, it is up to you. These are just words though, the important point is, that the motion is not directed when the speed of an object is zero.

Question 3. Again, I don't think there is a convention for this. Just say something like "it stopped moving, so direction is not defined."

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