# Scalar quantity, can it be negative?

1. Jun 3, 2010

### breeno

Alright, so a friend and I have been debating if a change in speed can be negative. I state that speed is final minus initial, which if the inital is low, the the speed will have dropped in magnitude.

He states that magnitude is absolute and no negatives are allowed.

I was under the belief that you can have a negative scalar, as it conveys an actual drop in the magnitude, whereas a negative vector requires direction.

Eg/. A ball is heading towards a wall at 3ms, and rebounds back at 3.5ms, what is it's change in speed?

2. Jun 3, 2010

### Stonebridge

Scalars can be negative, and so can a change in a scalar value.
Take temperature:
You can have a temperature of -10 degrees.
If temperature falls from 20 to 5 degress, the change was -15 degrees.
The negative value of the scalar is a consequence of where you take the "zero" to be.

With speed you have to be very careful because speed is the scalar bit of velocity. Velocity with no consideration of direction.

If a ball bounces from a wall as in your example, the change in speed was 0.5m/s, but the change in velocity was 6.5m/s
The confusion lies in the fact that, when you have velocity in just two dimensions, it is possible to express the direction by using + or - signs. To the left (or down) is plus, for example, and to the right (or up) is minus.
This is where it gets muddled with scalars.

3. Jun 3, 2010

### breeno

Thankyou, with regards to the question, I was under the belief that the change in speed was -0.5 (indicating the speed dropped by 0.5 with no regards to direction - my book also says -0.5), but the change in velocity was 6.5 (with regards to direction).

If I was to go into my exam using the "final minus intial (3 minus 3.5), would I be better off saying -0.5 (as per my book) or 0.5 in your opinion?

Last edited: Jun 3, 2010
4. Jun 3, 2010

### Stonebridge

In the question you wrote you gave the initial as 3 and the final as 3.5m/s (I didn't question how the ball could rebound faster than it hit)
If that was a typo and you meant it hit at 3.5 and rebounded at 3 then yes, the change in speed is -0.5m/s
Change is final - initial, always.

5. Jun 3, 2010

### breeno

Ah sorry, that must have been a typo, I meant initial as 3.5 and final as 3, sorry about that. Now I set out to shut that arrogant kid up! Thanks a lot for your help.

6. Jun 3, 2010

### poor mystic

Hi People
I believe that speed is the rate of change of position with respect to time. I believe that speed can only be positive, because it is equivalent to absolute velocity.

Can anyone cite some reference on this question?

May I add that change in speed can be negative, all the same.

7. Jun 3, 2010

### Stonebridge

There are a few things mixed in here that confuse the issue.
The title of the thread was about whether a scalar can be negative, although the question referred to speed, and mixed that in with "change in speed".
My first reply was to show that a scalar, in the case of temperature, can be negative, though it is a consequence of where you define the zero to be. The same is true for electrical and gravitational potential, for example.
Speed is normally always positive when taken purely as magnitude of velocity with no reference to direction.
As for definition: speed is rate of change of distance travelled with time, where distance is a scalar.
Velocity is rate of change of displacement with time, where displacement is a vector that measures a change in position in space.
http://physics.info/velocity/

8. Jun 3, 2010

### poor mystic

Hi All
I now wish to appeal to authority on the question of whether speed can be negative as Stonebridge asserts.
I say that a scalar is a pure number, positive or negative, which *scales* a vector.
I say that speed is not a scalar but is absolute velocity and is always positive, while velocity is a vector quantity in which a scalar is associated with a unit vector of velocity.

Then a change in speed can be positive or negative, though speed is always positive.
Stonebridge has pointed out that the title of the thread is misleading; I agree for the different reason that speed is not a scaler.

I see that Stonebridge and I have somehow taken different views on the correct answer to this question. As we cannot both be right and it does seem to be an important thing to be able to define speed correctly, I appeal to any authority that may be in a position to assist.

Last edited: Jun 3, 2010
9. Jun 3, 2010

### breeno

I think I've articulated myself poorly.

I acknowledge that speed is most likely and always will be a positive or absolute quantity. My argument with this other person was in relation to the given example, or more importantly a change in speed, which is the one thing we have all agreed that can be negative.

10. Jun 3, 2010

### Stonebridge

I don't think we disagree at all.
A scalar is a quantity that can be expressed purely as a single number (magnitude).
I said that a scalar (like temperature, gravitational potential)) can be negative, and that you have to be careful with speed because it is defined as the scalar (non directional) part of velocity, which is of course a vector.
[the negativity, as I said, is a consequence of how you define the zero]
A given negative speed would beg the question as to what the negative sign meant. If it refers in any way to direction then it is not a scalar we are talking about.
The link I gave explains this.
Speed is defined in relation to distance, a scalar; and velocity is defined in relation to displacement; a vector. It is a technical difference. Purely one of definition.
Look up any online physics dictionary for the definition of scalar, speed, velocity etc.
Alternatively, I'm sure someone on here with one of those self-appointed badges that says "Science Advisor/Resident Expert" or whatever will come along and pronounce.

11. Jun 3, 2010

### diazona

The badges are not self-appointed, by the way (if they were, everyone would have one )
Excellent point, and you are right. Speed is, by definition, the magnitude of velocity. And by definition, a magnitude cannot be negative, so speed cannot be negative. However, a change in speed can be positive or negative. As previously stated, change = final - initial, and if the initial value is larger than the final value, the change will be negative.

On a bit of a tangent: there is actually a stricter definition for "scalar" than just anything that isn't a vector. In introductory physics courses we often tell students that speed is a scalar, but technically that isn't true. Speed is the magnitude of a vector, which is its own kind of quantity.