Is there such a speed slower than no speed at all?

The speed is not negative the velocity is.

To say that a quantity is negative is to say that it is less than zero.  Velocity is a vector quantity.  Vectors are not totally ordered, and it is not meaningful to say that a velocity is less than another velocity, so it is meaningless to say that a velocity is negative.

If only I had been around earlier, you might not have wasted so much time trying to educate people.

Forgive me for jumping in the middle of this; the thought about slower than 0 has occurred to me a few times...and I have my 2 cents.

Yeah, it's all relative and stuff...but maybe there is just no movement. I'll just say that right now at my computer that I will stop movement within the universe. My chair along with Earth, the solar system, and the galaxy will fly away (i don't know how fast though). If I had a guess, I'd be going the average speed of everything. From the central point where the universe formed from...at creation or the big bang or whatever it's called, everything was pushed out in a somewhat uniform sphere. Where this sphere originated is what I would think zero movement would be.

But that's beside the point.

We know that the speed of light is relative. I slows down in water and glass...which is how it's refracted...and it's been sped up and stopped altogether in labs (at least, thats what they say).

Okay, so now I'm going to go the speed of light. According to Einstein I will have infinite mass.

Wait, though...is the speed of light 186000 mi/s...or have I already gone faster than the light did when it was stopped in that lab. I don't really remember achieving infinite mass.  

What this could mean, though, is that in our realm everything is going close enough to our own speed that we can interact with it.

While stopped, then, I may enter a new realm. In this realm the speed of light could be the same relative to their speed, but now I am moving in their realm. I will still exist in our present realm, but infinitely small. Again, I could go 186000 mi/s and enter a realm that we cannot interact with because we are infinitely small to it.

It's simple really, I'm just not sure I believe it.

None of that made sense.

As for the fighting that's going on considering negative velocity.



Consider two billiards balls.
Both weigh 5kg.
One is moving from the head of the table to the foot of the table at 5m/s.
The other is moving in the opposite direction from the foot of the table to the head of the table at 10m/s.
The two collide.
There is no friction and the collision is perfectly elastic with no loss of energy to heat.
What is the resulting velocity and momentum of each ball?

Try doing that problem without using a negative velocity and you'll see that negative velocities are necessary to describe relative motion opposite to the apparent motion or rest of another object.
You can't use E, W, N, or S in a math problem.

As for the fighting that's going on considering negative velocity.



Consider two billiards balls.
Both weigh 5kg.
One is moving from the head of the table to the foot of the table at 5m/s.
The other is moving in the opposite direction from the foot of the table to the head of the table at 10m/s.
The two collide.
There is no friction and the collision is perfectly elastic with no loss of energy to heat.
What is the resulting velocity and momentum of each ball?

Try doing that problem without using a negative velocity and you'll see that negative velocities are necessary to describe relative motion opposite to the apparent motion or rest of another object.
You can't use E, W, N, or S in a math problem.

The negative sign is used to show that one velocity is antiparallel to another.  Velocity is a vector quantity.

You lose.

Quote from: "midgard"

The speed is not negative the velocity is.

To say that a quantity is negative is to say that it is less than zero.  Velocity is a vector quantity.  Vectors are not totally ordered, and it is not meaningful to say that a velocity is less than another velocity, so it is meaningless to say that a velocity is negative.

If only I had been around earlier, you might not have wasted so much time trying to educate people.

He said it best.

Quote from: "Erasmus"

Quote from: "midgard"

The speed is not negative the velocity is.

To say that a quantity is negative is to say that it is less than zero.  Velocity is a vector quantity.  Vectors are not totally ordered, and it is not meaningful to say that a velocity is less than another velocity, so it is meaningless to say that a velocity is negative.

If only I had been around earlier, you might not have wasted so much time trying to educate people.

He said it best.

Duh!  It's Erasmus.

I've taken many years of physics.
This is so simple and that other guy has already shown very valid websites with diagrams that demonstrate this.
It is true that for any velocity in any direction, it may be described as a positive vector by assigning it a positive magnitude in the same direction as its movement.
However, in a free body system involving multiple moving bodies in the same vector axis but in opposite directions, you must describe them using the same direction, therefore one or the other must be described as negative.
Do you, at least, agree that there is such thing as negative acceleration?

I've taken many years of physics.
This is so simple and that other guy has already shown very valid websites with diagrams that demonstrate this.
It is true that for any velocity in any direction, it may be described as a positive vector by assigning it a positive magnitude in the same direction as its movement.
However, in a free body system involving multiple moving bodies in the same vector axis but in opposite directions, you must describe them using the same direction, therefore one or the other must be described as negative.

Dude, we just said the same thing, only you used a lot more words.

Do you, at least, agree that there is such thing as negative acceleration?

You mean deceleration? (Is instantly mobbed and beaten by the entire Physics staff at the college where he is going)

EXACTLY!
You DID say the same thing.
Negative velocity IS possible; it is a positive velocity in the OPPOSITE direction.
And no, I don't mean deceleration.
Deceleration is a word used by non-physicists do describe negative acceleration.
If I wanted to, I guess I could make the same kind of word for negative velocity.
From now on, negative velocity shall be known as "develocity".

Yay.

EXACTLY!
You DID say the same thing.
Negative velocity IS possible; it is a positive velocity in the OPPOSITE direction.
And no, I don't mean deceleration.
Deceleration is a word used by non-physicists do describe negative acceleration.
If I wanted to, I guess I could make the same kind of word for negative velocity.
From now on, negative velocity shall be known as "develocity".

Yay.

Dude, I know about the whole "deceleration" deal; hence why I wrote that stuff in parentheses.  I tried to make a funny.

I've taken many years of physics.

Wow.

it may be described as a positive vector by assigning it a positive magnitude in the same direction as its movement.

What other choice do you have, besides positive and zero, for magnitudes?  Magnitude cannot be negative.

What sort of magnitude do you have to assign to a vector (whatever that means) in order to allow you to describe the vector as negative?

(Haha.)

Is there anyone here who still believes there is no such thing as a negative velocity?

No?
Well, I'm glad that's all cleared up.

Yes, and I've studied physics at college too.

Surely a negative velocity is based purely on a subject human decisions of which direction is the "positive" direction, and another human could make the same subjective decision that the opposite direction is the positive direction.  Who is right?  Clearly from a scientific point of view, neither direction is positive or negative - they are simply in the direction that that are in, and in this context "positive" and "negative" simply refer to a direction, rather than a literal definition of those words.

Is there anyone here who still believes there is no such thing as a negative velocity?

/me raises his hand

The magnitude of a velocity is always positive by definition, but when you resolve in a particular direction (for example, the direction opposite to the direction of travel) you may obtain a negative value.

The negative sign does not mean that the velocity is negative - it simply refers to the direction that the velocity is in.  It's like how magnets are given a "North" and "South" pole.  Those terms typically have nothing to do with the actual directions "North" and "South" - it is simply a way of defining different directions relative to each other.  In this discussion we are clearly talking about "negative" in the context of negative numbers, rather than in the context of an arbitrary decision on which direction is the reference point.

Velocity includes direction. (common that's freshmen science at best) Without "what direction it's in" it's speed. So yeah it's still negative velocity.

The magnitude of a velocity is always positive by definition, but when you resolve in a particular direction (for example, the direction opposite to the direction of travel) you may obtain a negative value.

a negative value for what?

To anybody who wants to say that velocities can be negative, I would ask you to please define what it means for anything to be negative.

a negative value for what?

The velocity

To anybody who wants to say that velocities can be negative, I would ask you to please define what it means for anything to be negative.

I define negative as the opposite of positive. Isn't that helpful? It's like the charges on a magnet: positive and negative.

As I said, the way that velocity is defined in physics means that you can have a negative velocity. It's not a negative speed but as speed and velocity aren't the same thing so that's a mute point.

In regards to beast pointing out that negative velocity is subjective I totally agree. Of course I'm curious as to why he can't see that positive velocity is also subjective (meaning all direction is subjective).

---

Little quiz:

I am at point A, I move from point A towards point B for 100 metres in a minute. I stay at point B for another 20 minutes. What is my average velocity in metere/minute?

I wonder if we are at a full stop, is there something slower?

If one was going a negative speed, then that would mean he or she would be traveling backwards in time.

Quote from: midgard

The speed is not negative the velocity is.

To say that a quantity is negative is to say that it is less than zero.  Velocity is a vector quantity.  Vectors are not totally ordered, and it is not meaningful to say that a velocity is less than another velocity, so it is meaningless to say that a velocity is negative.

If only I had been around earlier, you might not have wasted so much time trying to educate people.

Never once have I said that a negative velocity is a negative quanity (that I recall), only an opposite direction. Speed is the component of velocity that determines its quantitive value and cannot be less than zero, this is correct. But the other component of speed is direction and every direction has an opposite direction. You can't just discount the direction and say because the quantitive value of velocity can't be negative then neither can the velocity itself.

Perhaps if Negative Velocities were written differently you, beast, etc. wouldn't get so confused.

Can you see that a velocity of -10m/s D (D for direction) is not saying that the speed (note choice of words) is negative but the direction. Would it help clear things up if instead of writing it -10m/s D it was written 10m/s -D?

Never once have I said that a negative velocity is a negative quanity (that I recall), only an opposite direction. Speed is the component of velocity that determines its quantitive value and cannot be less than zero, this is correct. But the other component of speed is direction and every direction has an opposite direction. You can't just discount the direction and say because the quantitive value of velocity can't be negative then neither can the velocity itself.

Perhaps if Negative Velocities were written differently you, beast, etc. wouldn't get so confused.

Can you see that a velocity of -10m/s D (D for direction) is not saying that the speed (note choice of words) is negative but the direction. Would it help clear things up if instead of writing it -10m/s D it was written 10m/s -D?

What you're actually saying is that the D component of the velocity(the velocity along your self imposed D axis) is -10m/s.  You're not actually saying that the velocity vector itself is negative. 

Remember that for a standard Cartesian coordinate system (x,y,z) the velocity vector is:
v=(dx/dt)i+(dy/dt)j+(dz/dt)k
All three components of the velocity can be negative, but that doesn't mean the vector is negative. 

That all being said.  When talking about rectilinear motion along an axis it is perfectly acceptable to represent the velocity as a positive or negative scalar value since the direction is fixed. 

Quote from: Robin S

The magnitude of a velocity is always positive by definition, but when you resolve in a particular direction (for example, the direction opposite to the direction of travel) you may obtain a negative value.

a negative value for what?

For the component of the velocity in the direction you have resolved.

Say that we define a fixed cartesian co-ordinate system for our velocity to be measured relative to (since all velocities must be measured relative to something). Then, taking the units of metres per second resolved parallel to the x, y and z axes, it is entirely possible that we will obtain three negative values. In other words, starting at the origin and allowed to travel for 1 second, our object might end up at the position (-3,-2,-5). The magnitude of its velocity would still be positive (in this case, sqrt38 metres per second) but we have resolved it in directions which give negative components. There is no contradiction at all here, since we are measuring two different aspects of the velocity: its magnitude, and its components parallel to fixed axes.

I think more interesting than the OP is, "Is there such a speed as no speed at all?"

Since all speeds are only measurements based on relativity to an observer, is there really a 0?

Relative to the observer their can be. And since i am the observer, and only i matter... yes.

Velocity is a vector and therefore relates to speed and direction, therefore in velocity you can go into the negatives.

Speed, however, is not a vector and only relates to distance travelled over time, not in what direction, and therefore cannot be less than zero.

Velocity is a vector and therefore relates to speed and direction, therefore in velocity you can go into the negatives.

Speed, however, is not a vector and only relates to distance travelled over time, not in what direction, and therefore cannot be less than zero.

A negative vector is mathematically possible, but it does represent poor notation and should always be avoided. We have a set of all possible vectors consisting of only positive vectors, introducing negative vectors into that set is redundant.

Quote from: Trekky0623 on November 17, 2007, 09:21:14 AM

Velocity is a vector and therefore relates to speed and direction, therefore in velocity you can go into the negatives.

Speed, however, is not a vector and only relates to distance travelled over time, not in what direction, and therefore cannot be less than zero.

A negative vector is mathematically possible, but it does represent poor notation and should always be avoided. We have a set of all possible vectors consisting of only positive vectors, introducing negative vectors into that set is redundant.

Redundant but possible. Therefore you CAN have a negative vector. so let's just drop it.

The question was about negative speed anyways and we've already proven that no you can't have a negative speed without time travel so this debate should be over.