# Directions of velocity and acceleration

Can anyone help me with this?

If we use plus and minus signs to indicate teh directions of velocity and acceleration, in which of the following situations does the object speed up?
a. positive velocity and negative acceleration
b. negative velocity and positive acceleration
c. positive velocity and zero acceleration
d. negative velocity and negative acceleration

thank you!!!!

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b.

positive acceleration equals speeding up
negative acceleration means slowing down and eventually opposite direction
0 acceleration is constant speed so nothing happens

current velocity doesn't matter.

soljaragz said:
b.

positive acceleration equals speeding up
negative acceleration means slowing down and eventually opposite direction
0 acceleration is constant speed so nothing happens

current velocity doesn't matter.
Current velocity DOES matter. Positive acceleration is acceleration in the +ve direction, and negative acceleration is acceleration in (duh) the -ve direction. If we are travelling at a positive speed and accelerate in that same direction, clearly we're going to speed up. If we're travelling at a negative speed and accelerate in the negative direction, what will happen?

huh?? ... THANKS, I guess I misread stuff.

Positive speed, negative speed? Speed is never negative.
I think I understand what you are trying to say but the used terminology is absolutely wrong.

Kurdt
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Velocity can be negative depending on the coordinate system you use. Say for instance you define an x-axis going from left to right down your street. Any car travelling from left to right has a positive velocity wrt your x-axis. Any car travelling right to left has a negative velocity wrt your x-axis. Speed is the magnitude of the velocity vector and thus is always positive but the question was involving velocities not speed which require directional information also.

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Kurdt said:
Speed can be negative depending on the coordinate system you use. Say for instance you define an x-axis going from left to right down your street. Any car travelling from left to right has a positive speed wrt your x-axis. Any car travelling right to left has a negative speed wrt your x-axis.
Sorry but this is absolutely incorrect.
It seems you mix up physics with mathematics. In nature there is no such thing as negative speed.

Teaching students that negative speed is a physical quantity is doing a great disservice to the understanding of natural phenomena.

Kurdt
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You sufficiently confused me to post speed before I managed to edit it and then beat my editing with that post but I do realise the distinction.

You're right, it was a misnomer on my part. I should have said positive and negative velocity. Speed, being a scalar quantity, is inherently positive whereas velocity, being a vector quantity, can be positive or negative. That said, once you're used to the terminology they get interchanged quite often.

arildno
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Hawknc said:
Speed, being a scalar quantity, is inherently positive whereas velocity, being a vector quantity, can be positive or negative. .
Again, incorrect!
In general, only scalar quantities can be either positive or negative (it can also be zero).
Speed is, by definition, a non-negative scalar quantity.

Only in the special case where we are to compare parallell and anti-parallell vectors is it meaningful of talking of the vector quantity as "positive", or "negative", by which it is meant that one of the direction is labeled "positive", the other as "negative".

lol, and the award for greatest self-pwnage goes to me for improperly explaining myself again. ;)

Speed is inherently positive, as I said. Something like temperature, for example, can be positive or negative but is still scalar. Should've said magnitudes and directions instead. Velocities can certainly be negative, though, depending on the frame of reference. A vector a = -2i is negative when compared to b = 2i, isn't it?

arildno
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Quite so!

But it isn't meaningful to try to find out which of the vectors 2j, -3i, 2i-7j are to be regared as negative or positive.

nrqed
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arildno said:
Quite so!

But it isn't meaningful to try to find out which of the vectors 2j, -3i, 2i-7j are to be regared as negative or positive.
Hear hear!

It always bothers me when people talk about vectors being negative or positive! The only things that may be positive or negative are the *components* of the vectors.

What happens, of course, is that in 1-D, one can eschew a vector for its (unique) component so it is tempting to stop saying "the x component of the velocity is negative", for example and to say instead "the velocity is negative". Unfortunately doing so leads to a very bad habit!
As a low-level physics teacher I myself struggle with this.

To the OP: The answer is that, for motion in one dimension, an object will speed up when the acceleration and velocity vectors point in the same direction (or, in other words, when their components have the same sign )

AND an object will speed up when there is an acceleration and the velocity vector is zero.

This sometimes surprises people because that implies that an object *may* speed up even if its acceleration is *negative*! Indeed, an object with a negative component of the acceleration *will* speed up if the x component of the velocity is negative itself.

On the other hand, if the components of the acceleration and velocity are of opposite signs, the object will slow down.

So the most general result is this:

A) x components of velocity and acceleration of opposite signs -> object slows down

B) x and y components of velocity and acceleration of the same sign -> object speeds up

C) velocity zero but acceleration non-zero -> object speeds up

D) acceleration zero but velocity zero -> motion at constant speed

E) both velocity and acceleration zero -> well, that should be obvious Patrick

Hawknc said:
Something like temperature, for example, can be positive or negative but is still scalar.
Again I have to respectfully disagree strongly. Temperature can never be negative.

Teaching students that temperature can be negative because we use those absurd Celsius and Fahrenheit scales is placing the horse behind the carriage and doing no service to their understanding of the matter.

arildno
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There is nothing absurd about using the Celsius scale.

This is getting beyond the point of the thread, but it's still negative. Is it a silly scale? Absolutely, and I'd prefer that Kelvin was used to be honest, but negative all depends on where you set your zero. If it's set at 273.15K, then any temperature below that is negative in Celsius. It was an off-the-cuff example, admittedly, but it's a bit hard to deny that -4 degrees C exists, even if only in a silly but widely used form.

Kurdt
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spot the pure mathematicians contest! Geez guys calm.

nrqed
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MeJennifer said:
Again I have to respectfully disagree strongly. Temperature can never be negative.

Teaching students that temperature can be negative because we use those absurd Celsius and Fahrenheit scales is placing the horse behind the carriage and doing no service to their understanding of the matter.
What is the mathematical definition of something being "absurd"? Either something is correct or it's incorrect (or it's unprovable :-)). There is no place for "absurd". Absurd refers to a question of personal taste so it's irrelevant if someone finds something absurd or not. There is nothing wrong with the Celsius scale.

Going back to the definition of a scalar quantity...As a general definition, a scalar quantity may either be positive or negative, no?

nrqed said:
What is the mathematical definition of something being "absurd"? Either something is correct or it's incorrect (or it's unprovable :-)). There is no place for "absurd". Absurd refers to a question of personal taste so it's irrelevant if someone finds something absurd or not. There is nothing wrong with the Celsius scale.
Imagine we would do the same thing for mass. Say 0 gram is defined as the mass mount Everest. Then both of us would have a negative mass. And then the question how much is twice as heavy as mount Everest? 2 x 0?
And that would not be a problem to you? No ontology issues for you?
Well in that case we can agree to disagree. :)

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nrqed
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MeJennifer said:
Imagine we would do the same thing for mass. Say 0 gram is defined as the mass mount Everest. Then both of us would have a negative mass. And that would not be a problem to you? No ontology issues for you?
Well in that case we can agree to disagree. :)
I guess we will have to agree to disagree, indeed:shy:

There is no mathematical problem with assigning the zero scale of mass to any value. But yes, it is more convenient and more meaningful physically to assign it to the absence of mass. So the first thing is to distinguish mathematical criteria from physical criteria. My main point is that mathematically, a scalar may be either positive or negative. Do you agree on this point?

The second issue is the question of temperature, why would the Kelvin scale be "less absurd"? Playing the devil's advocate , I could ask the following question: what is the physical meaning of T=0 in the Kelvin scale? It actually does not exist, right? On the other hand, the T=0 point of the Celsius scale if physically well defined and can be set very precisely in a lab. So based on *that* criterion, one could argue for a the Celsius scale being "less absurd" than the Kelvin scale. In that sense, the comparison with mass is not quite fair.

Regards

Patrick

nrqed said:
My main point is that mathematically, a scalar may be either positive or negative. Do you agree on this point?
Yes, but how is that relevant to physics? Math and physics are two entirely difference things. One simply uses math as a tool in physics. And apparently some do not even understand the suitability of selection of scale in cases of temperature.

The second issue is the question of temperature, why would the Kelvin scale be "less absurd"? Playing the devil's advocate , I could ask the following question: what is the physical meaning of T=0 in the Kelvin scale? It actually does not exist, right? On the other hand, the T=0 point of the Celsius scale if physically well defined and can be set very precisely in a lab. So based on *that* criterion, one could argue for a the Celsius scale being "less absurd" than the Kelvin scale. In that sense, the comparison with mass is not quite fair.
Really now? 0 Celcius is "well defined" while 0 Kelvin is not? 0 Kelvin is very well defined in classic theory.
Of course the uncertainty principle will disallow making something 0 Kelvin for any lenght of time but the same goes here for 0 Celsius. But presumably that would go for mass as well.

Anyway there is no point in arguing with you on this.
Keep telling students that temperature, speed, mass etc can be negative because one can make a scale in "almighty" math that would make it so. Last edited:
nrqed
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MeJennifer said:
Yes, but how is that relevant to physics? Math and physics are two entirely difference things. One simply uses math as a tool in physics. And apparently some do not even understand the suitability of selection of scale in cases of temperature.
Sorry, I had been left with the impression that your first post on this topic was disputing the idea of scalars being possibly negative. But I see that your objection was purely concerning temperature. Sorry about that.
Really now? 0 Celcius is "well defined" while 0 Kelvin is not? 0 Kelvin is very well defined in classic theory.
Even within classical physics, one would one go about obtaining a system strictly at zero Kelvin? even within classical physics, the zero scale of the Kelvin scale is much more difficult to obtain in a lab than the zero of the Celsius scale, would you dispute that?

You are saying that we are talking about physics here and not maths. Then wouldn't you agree that from a physical point of view (and physics is ultimately about experiments and measurements), the zeroth of the Celsius scale is much more "physical" than the Kelvin scale???? Of course the uncertainty principle will disallow making something 0 Kelvin for any lenght of time but the same goes here for 0 Celsius. But presumably that would go for mass as well.
Well that would be a totally different scale but QFT has no problem dealing with massless particles (e.g. photons) so I am not sure what the last statement is about. (unless one gets into quantum gravity stuff). But that's a whole different thread.
Anyway there is no point in arguing with you on this.
Keep telling students that temperature, speed, mass etc can be negative because one can make a scale in "almighty" math that would make it so. :surprised I never said that speed could be negative. By its very definition it cannot be negative.

But you are right, given your tone :yuck: there is no pooint discussing this with you.

Patrick

nrqed said:
I never said that speed could be negative. By its very definition it cannot be negative.
So then what about temperature? How could temperature possibly be negative? What else is temperature than random motion of matter particles? You are saying that we are talking about physics here and not maths. Then wouldn't you agree that from a physical point of view (and physics is ultimately about experiments and measurements), the zeroth of the Celsius scale is much more "physical" than the Kelvin scale????
It seems that you do not understand it one bit. For temperature it is simply more suitable to have a scale that starts with zero, this reflects much better the natural phenomenon we attempt to model here. Zero being the state of no average motion of mass particles. Such a scale exist and it is the Kelvin scale. It seems that you grasp it with speed but not with temperature.

Amazing, I have to argue on a science forum with someone claiming the Celsius scale is more appropriate than the Kelvin scale. Last edited:
Could we just pretend I said "speed is a scalar AND is inherently positive" so this never happened? Hawknc said:
Could we just pretend I said "speed is a scalar AND is inherently positive" so this never happened? Well, speed is not a scalar, speed is a natural phenomenon.
Now that we model that in a particualr way is an entirely different issue altogether. Natural phenomena are not mathematical things. See my point? 