# Change of direction in physics

## Main Question or Discussion Point

Hi, this problem is making my head ache.

Lets say that an object is moving at a decelerating speed(-1m/s) starting on 4m/s towards east and stopped after 4 seconds.
(There are no friction.)

After 4 seconds, the object would have 0 speed, no direction and 0 velocity etc.

Question 1 : Is the object 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 The vector changes to a null vector too.

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

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Hi, this problem is making my head ache.

Lets say that an object is moving at a decelerating speed(-1m/s) starting on 4m/s towards east and stopped after 4 seconds.
(There are no friction.)

After 4 seconds, the object would have 0 speed, no direction and 0 velocity etc.

Question 1 : Is the object 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 The vector changes to a null vector too.

Sorry for the bad english..... it isn't my native language
Hi... I also does not know the exact answer... but let us try to solve it together... So we have an object which is decelerating at 1 m/s with initial velocity of 4 m/s.... So the direction of the vector is east and velocity is 4. In one second, the velocity is 3 and direction is east. We need this information because when you try to add another vector to this to find the resultant, you need both the direction and magnitude to do it.... So east will tell you that if you add another vector which acts towards west, the magnitude will have to be subtracted to give the resultant.... However in your case, at the end of 4 seconds, when the magnitude is no longer a value, the object can be said to be at absolute rest (with respect to whatever frame of reference we are using).... So it becomes a null vector without any direction or magnitude... It means you are defining the presence of a vector in a vector field which has no magnitude and direction but has a position....

A null vector will thus have no value but could potentially attain any direction....

Hi... I also does not know the exact answer... but let us try to solve it together... So we have an object which is decelerating at 1 m/s with initial velocity of 4 m/s.... So the direction of the vector is east and velocity is 4. In one second, the velocity is 3 and direction is east. We need this information because when you try to add another vector to this to find the resultant, you need both the direction and magnitude to do it.... So east will tell you that if you add another vector which acts towards west, the magnitude will have to be subtracted to give the resultant.... However in your case, at the end of 4 seconds, when the magnitude is no longer a value, the object can be said to be at absolute rest (with respect to whatever frame of reference we are using).... So it becomes a null vector without any direction or magnitude... It means you are defining the presence of a vector in a vector field which has no magnitude and direction but has a position....

A null vector will thus have no value but could potentially attain any direction....
What I am most troubled about is :
Does the Direction Change in the Course of the object stopping(put at an absolute rest)?
Like, The first vector is 4m/s to east and in the very moment the object stops, the vector changes to a null vector without a direction.
In that very moment(the change of vector), can I say that the direction has 'changed'?

What I am most troubled about is :
Does the Direction Change in the Course of the object stopping(put at an absolute rest)?
Like, The first vector is 4m/s to east and in the very moment the object stops, the vector changes to a null vector without a direction.
In that very moment(the change of vector), can I say that the direction has 'changed'?
Hmmm... k.... So what will happen if it is a direction change. A force has to act on an object to cause change in direction. Since your object is decelerating, there is a force acting on it (though you said there is no friction) and hence if the change from motion to rest is termed as direction change, I don't find any violation in the laws of physics... But I don't really know, that is how people look at it... As far as I know, the direction 'East' is now potentially 'direction all' for the object.

Hello,

One opinion:

In physics, we refer to Euclidean vector (geometric) as a physical quantity with magnitude and direction. Your car is represented by a bound vector because it has an origin and kept the same direction (eastward) all the time.
To decelerate the car means to diminish the vector's magnitude. No other vector needs be involved. There is no change in direction, just in magnitude.

In response to question 2,
Hi, this problem is making my head ache.

Lets say that an object is moving at a decelerating speed(-1m/s) starting on 4m/s towards east and stopped after 4 seconds.
(There are no friction.)

After 4 seconds, the object would have 0 speed, no direction and 0 velocity etc.

Question 1 : Is the object 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 The vector changes to a null vector too.

Sorry for the bad english..... it isn't my native language
Consider this equivalent to having a positive number,and reducing its value,making it approach zero.What you're asking is,after the number becomes 0,has its sign changed?

Question 1 : Is the object a null vector(0 vector) after it completely stops?
Sorry, I overlooked the first question.

A null vector has magnitude - it is zero.
But it has no direction.

In response to question 2,

Consider this equivalent to having a positive number,and reducing its value,making it approach zero.What you're asking is,after the number becomes 0,has its sign changed?
Hmmm
I learned at math class that 0 is not positive or negative.
It's just 0 nothing more.

I got a reply from a professor I know :

An important concept is velocity. Velocity is a vectorthat points in the direction of travel of the object and its magnitude is the speedof the object.

When the movement of the object stops, the velocity will be (in, say, three dimensions) v⃗ =(0,0,0). That is probably what you mean by null vector.

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 right → going nowhere} a direction change, it is up to you.

• Premanand
Hmmm
I learned at math class that 0 is not positive or negative.
It's just 0 nothing more.
Hmmm.... What do you think will happen if I assume the vector as 0 east or 0 west ? All are trying to say that since it is a null vector and the magnitude is zero , it doesn't matter in which direction it acts. However , your question as I understand is ' should I take the loss in direction as change in direction ? '

Hmmm.... What do you think will happen if I assume the vector as 0 east or 0 west ? All are trying to say that since it is a null vector and the magnitude is zero , it doesn't matter in which direction it acts. However , your question as I understand is ' should I take the loss in direction as change in direction ? '
Yes!!
That's what I meant all along..

Hmmm.... What do you think will happen if I assume the vector as 0 east or 0 west ? All are trying to say that since it is a null vector and the magnitude is zero , it doesn't matter in which direction it acts. However , your question as I understand is ' should I take the loss in direction as change in direction ? '
I'm trying to answer this question because it's a test problem... I need to hand it back till tomorrow.
I need to prove my point that loss in direction means a change in direction.........

Dale
Mentor
The direction of a null vector is undefined. As a result, any comparison of direction with a null vector is also undefined.

The direction of a null vector is undefined. As a result, any comparison of direction with a null vector is also undefined.
Hi ... Can the change in direction happen without affecting the magnitude in case of linear motion ? Is there any example for it ? All that I could think of is a circular motion where there is a continuous change of direction without change in magnitude ...

Dale
Mentor
I am not certain, but I am guessing that you are assuming continuity. In 1D motion, direction itself is discontinuous. So any change in direction will be discontinuous also.

I am not certain, but I am guessing that you are assuming continuity. In 1D motion, direction itself is discontinuous. So any change in direction will be discontinuous also.
Thank you... I asked it because in linear motion any deceleration can potentially change the direction after a period of time once the magnitude diminishes to zero... For instance, as juyoung said, the magnitude which was +5 became zero in time '5 sec' , could have potentially reversed the direction with a vector value of '-1' in the 6th second isnt it? So is it not the zero magnitude is like transition phase? So can he conclude that in linear motion specific to the condition defined by him, the zero magnitude & directionless null vector is a beginning of time period where there could be a potential change in direction?

CWatters
Homework Helper
Gold Member
I need to prove my point that loss in direction means a change in direction..
What happens after the velocity reaches zero? It's possible for it to increase again in any direction including the original direction. All you can say is that at zero velocity the direction is undefined. You can't say it definitely does change direction.

Dale
Mentor
So is it not the zero magnitude is like transition phase?
I think the term you are looking for is "discontinuity".

• Premanand
Question 1 : Is the object 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 The vector changes to a null vector too.
1. Physically, no-motion and no-direction make a vector non-existent.
Mathematically, a vector with no magnitude does not perform any function, and we call it the null vector. It is like your car sitting and figuring out which way to go: when you start the engine (preparing the magnitude) you need to decide where to go (direction). Revving up the engine and sitting because you haven't made up your mind means that your direction is not defined.

2. Displacement, velocity (both average and instantaneous), and acceleration - all are vectors, and all require the mention of a direction in order to fully describe the quantity. Otherwise, they would be scalars, which you get when you read the gauges on your dashboard - no instrument tells you which way you are going. You would have to also read a compass for that.
In your case, only acceleration vector changes direction.
The displacement and velocity maintain their direction.

But if you insist in being correct, you will have to re-define several mathematical and physical concepts involved here.
Can you?

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