Directions of velocity and acceleration

[uwmphysics]

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!

 

[soljaragz]

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.

 

[Hawknc]

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 traveling at a positive speed and accelerate in that same direction, clearly we're going to speed up. If we're traveling at a negative speed and accelerate in the negative direction, what will happen?

 

[soljaragz]

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

 

[MeJennifer]

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]

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 traveling from left to right has a positive velocity wrt your x-axis. Any car traveling 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.

 

[MeJennifer]

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 traveling from left to right has a positive speed wrt your x-axis. Any car traveling 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]

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

 

[Hawknc]

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]

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".

 

[Hawknc]

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]

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]

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

 

[MeJennifer]

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]

There is nothing absurd about using the Celsius scale.

 

[Hawknc]

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]

spot the pure mathematicians contest!

Geez guys calm.

 

[nrqed]

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?

 

[MeJennifer]

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. :)

 

[nrqed]

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

 

[MeJennifer]

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 length 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.

 

[nrqed]

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 length 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.

I never said that speed could be negative. By its very definition it cannot be negative.

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

Patrick

 

[MeJennifer]

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.

 

[Hawknc]

Could we just pretend I said "speed is a scalar AND is inherently positive" so this never happened?

 

[MeJennifer]

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 particular way is an entirely different issue altogether.
Natural phenomena are not mathematical things. See my point?

 

[nrqed]

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.

Yes, but one has to be clear with the maths concepts before using math terminology in physics. So it's not a waste of time to get the math right.

And apparently some do not even understand the suitability of selection of scale in cases of temperature.

So you would tell your students that negative temperature are *impossible*?

Btw, have you ever heard of spin systems in which the thermodynamic temperature may be negative (because putting in more energy may decrease the number of microstates available)? If not, you should look this up.

Really now? 0 Celcius is "well defined" while 0 Kelvin is not?

If the criterion is to be able to measure something experimentally, then the O Celsius point *is* well defined experimentally. Tell mw how to go in the lab and obtain a system at 0 Kelvin?
You are the one who keep insisting that math is secondary and that physics comes first. Then what is so horrendous about a scale which has a zero that is accesible experimentally? The zeroth of the Kelvin scale is a theoretical construct.

0 Kelvin is very well defined in classic theory.
Of course the uncertainty principle will disallow making something 0 Kelvin for any length 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.

That's so incredibly childish...to put words in my mouth. As if I had argued that I wanted to allow for negative speed and negative mass. Please be more mature and don't put words in my mouth.
By the way, your comparison with mass (and doubling the mass of the Everest using 2 x 0 ) is inappropriate because this mass and temperature are not both extensive quantities.


But if I am to join the ranks of people on this site you consider stupid, I am in good company (I resisted the temptation to give links to some of your other arrogant posts).

Have a good day

 

[MeJennifer]

So you would tell your students that negative temperature are *impossible*?

Yes! Just like I would tell them that negative mass and negative speed are impossible. Furthermore I would explain them that in science cold is not the opposite of hot. Everything is hot, only in different degrees.

I would tell them as well that unfortunately some people in history have developed inappropriate scales that map certain temperatures as negative.

As if I had argued that I wanted to allow for negative speed and negative mass. Please be more mature and don't put words in my mouth.

Feel free to demonstrate the logic in finding the idea of negative speed and negative mass inappropriate while seeing no problem with negative temperature.

But if I am to join the ranks of people on this site you consider stupid, I am in good company.

I do not consider you stupid.
But it seems you are a bit indifferent to the phenomenon of temperature, it seems you rather focus on the math.
Let me include some quotations to explain what I am referring to:

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.

Here you are clearly disconcerned about the suitability of a particular scale. Imagine we would do the same thing for mass or speed!

There is no mathematical problem with assigning the zero scale of mass to any value.

Here again you are only concerned with "if the math works". I am fully aware that there is no mathematical problem. That is until (hypothetically of course) we would have a true negative temperature in nature, then unfortunately we would have used up the negative sign already.

Your argument goes like: "Sure temperature can be negative, here let me make a scale for you to demonstrate it! The math works, so who cares!".
My point is: "Just the fact that we can model it as such in math does make it so for the phenomenon in nature. And some models are simply more appropriate than others as is the case with the Kelvin scale".

Ultimatelty, in nature temperature cannot be negative, the why would you want to use a scale that would use negatives for temperature?

By the way, you are entitled to your opinion and I respect it!
As far as I am concerend there is no need for name calling and so, we simply have a friendly discussion about a disagreement.

 

[Kurdt]

MeJennifer:

Scales are arbitrary anyway. There is no point saying that everything should be set at the what YOU consider the correct scale. There are many situations where it is advantagous to change the zero point of a particular scale. For instance in energy levels of a hydrogen atom it is advantageous to set the lowest energy level to zero. The physics isn't any different you just get different numbers out of it. I don't understand your grievance and I pity your students. Personally I think this argument is going nowhere. If you believe in using set scales when its easier to change them then fair enough but it is not wrong for anyone else to do otherwise.

 

[borisleprof]

Speed or velocity?
speed is magnitude of the velocity vector. So speed is always a positive quantity.
Now along a line we define the acceleration as a =(vf-vi)/t, (or delta t).
Along a line you define a positive and a negative sens.

if along this line a > 0 then the object is spreeding up along this line and the acceleration is directed along the positive sens.