Is velocity ever a scalar quantity?

[Charles Link]

It may be of interest to the OP that English uses the word velocity to indicate it being a vector and the word speed when referring to the magnitude of the velocity vector. From what I have read, the German language doesn't have the distinction of these two and uses the word Geschwindigkeit for both velocity and speed. They then need to specify whether they are referring to the vector, or its magnitude. In any case, I thought the inputs above were very good, and did a good job explaining how velocity, except when used very loosely, refers to a vector.

Edit: @fresh_42 You have German as your native language= Gibt es nur das einzige Wort Geschwindigkeit? (Is there only the one word Geschwindigkeit?)

 

[Orodruin]

It may be of interest to the OP that English uses the word velocity to indicate it being a vector and the word speed when referring to the magnitude of the velocity vector. From what I have read, the German language doesn't have the distinction of these two and uses the word Geschwindigkeit for both velocity and speed. They then need to specify whether they are referring to the vector, or its magnitude. In any case, I thought the inputs above were very good, and did a good job explaining how velocity, except when used very loosely, refers to a vector.

Interesting. In Swedish we have distinct words: hastighet and fart. Usually words are pretty 1-1-mapped to German …

(We also have a saying that translates funnily to Swenglish:
Det är inte farten som dödar, det är smällen. -> It is not the fart that kills, it is the smäll.
”Smäll” being pronounced as ”smell” and being Swedish for ”impact”)

 

[blue raven]

To understand what velocity is, would be quite useful a diagram, such as the one below. By the way, speed is not the magnitude of velocity.

A car starts to move with a constant speed from point A to point B, passing through the intermediate point C on this gray road. Velocity is defined as a vector, $\vec{v}$ , which means it has one direction and one magnitude. Velocity is calculated as displacement (blue vector) $\vec {d}_{AB}$ divided by time, regardless of the length of the path ACB.
$$\vec{v}=\dfrac{\vec{d}_{AB}}{t}$$
This is the magnitude of the vector velocity, and it is not the speed of the car.
Speed is the one defined (or achieved) on the curved path ACB. A car can accelerate from A to C, and its speed is calculated using this distance, using suvat. You cannot calculate the magnitude of the vector velocity using suvat because the displacement AB is different from the path ACB. The only possibility to have speed=velocity would be a straight gray path from A to B. And by the way, a line that has one dimension 1D (just length), do not imply that this line is not curved in 2D or 3D.
So it seems that Khan is right. You can calculate the magnitude of the vector velocity $\vec{v}$ only if you know the magnitude of the displacement vector $\vec{d}$ .

 

[Charles Link]

I disagree completely=the velocity vector changes direction as the car goes through this curved path, but I think even you probably know that.

 

[blue raven]

And the direction of vector velocity $\vec{v}$ is given by what? By vector displacement $\vec{d}$. You can find the vector displacement only when you choose two points A and B on the curved gray path. So, this is exactly what I did, I have chosen two points on the gray path. When the car travels from A to B, this is the vector velocity, it has one direction and one magnitude, not two, not three.

 

[Orodruin]

And the direction of vector velocity $\vec{v}$ is given by what? By vector displacement $\vec{d}$. You can find the vector displacement only when you choose two points A and B on the curved gray path. So, this is exactly what I did, I have chosen two points on the gray path. When the car travels from A to B, this is the vector velocity, it has one direction and one magnitude, not two, not three.

You are thinking of average velocity over some finite time. This is not how instantaneous velocity is defined - it is defined as a limit when the time interval goes to zero. Speed is defined as the magnitude of instantaneous velocity. Simple as that.

Claiming something else is just wrong.

 

[robphy]

The velocity vector at a given time is a tangent vector to the trajectory (which gotten by taking the limit mentioned by @Orodruin ).

 

[blue raven]

You are thinking of average velocity over some finite time. This is not how instantaneous velocity is defined - it is defined as a limit when the time interval goes to zero. Speed is defined as the magnitude of instantaneous velocity. Simple as that.

Claiming something else is just wrong.

So Encyclopedia Britannica is wrong?
"Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object’s movement. Put another way, speed is a scalar value, while velocity is a vector. For example, 50 km/hr (31 mph) describes the speed at which a car is traveling along a road, while 50 km/hr west describes the velocity at which it is traveling."
https://www.britannica.com/story/whats-the-difference-between-speed-and-velocity

NASA about instantaneous velocity, does not say anything about any speed. Please provide a credible link for your allegation.
The velocity -V of the object through the domain is the change of the location with respect to time. In the X - direction, the average velocity is the displacement divided by the time interval:
V = (x1 - x0) / (t1 - t0)
This is just an average velocity and the object might speed up and slow down between points "0" and "1". At any instant, the object could have a velocity that is different than the average. If we shrink the time difference down to a very small (differential) size, we can define the instantaneous velocity to be the differential change in position divided by the differential change in time;
V = dx / dt
https://www.grc.nasa.gov/www/k-12/airplane/disvelac.html
Velocity vs speed
https://www.physicsclassroom.com/class/1dkin/lesson-1/speed-and-velocity

 

[weirdoguy]

So Encyclopedia Britannica is wrong?

Encylopedia Britannica contradicts what you said. Read your sources. You are wrong, according to them!

Please provide a credible link for your allegation.

Every textbook on basic physics that uses calculus. Please mind you, a lot of us are physicists, we kind of know what we are talking about. I don't like arguments from authority, but we are talking about one of the most basic things in physics, and you seem to be a little too argumentative.

 

[blue raven]

The velocity vector at a given time is a tangent vector to the trajectory (which gotten by taking the limit mentioned by @Orodruin ).

This is correct, but again a diagram would be quite useful to understand the difference between average velocity versus instantaneous velocity, such as the one below.

The vector velocity $\vec{v}$ is given by the vector displacement $\vec{d}$. When we reduce the distance between the two points, this vector comes closer to the apex of the curve. We move the displacement from AB to CD to EF, and then the two last points GH are very close. Now the last displacement vector $\vec{d}_{4}$ is tangent to the path indeed, while it becomes very small. So this is the explanation.

 

[Orodruin]

This is correct, but again a diagram would be quite useful to understand the difference between average velocity versus instantaneous velocity, such as the one below.
View attachment 355625

The vector velocity $\vec{v}$ is given by the vector displacement $\vec{d}$. When we reduce the distance between the two points, this vector comes closer to the apex of the curve. We move the displacement from AB to CD to EF, and then the two last points GH are very close. Now the last displacement vector $\vec{d}_{4}$ is tangent to the path indeed, while it becomes very small. So this is the explanation.

The displacement becomes small, but so does the time. These two effects will cancel ouf to give a finite velocity.

You also do not need to approach the apex. The velocity along your curve will be different depending on the position you consider.

Please provide a credible link for your allegation.

Any basic textbook on classical mechanics will do. Try Landau-Lifshitz or the Feynman lectures on physics for example. There really is no way of saying this but you are simply wrong and any introductory textbook will tell you so.

 

[blue raven]

You are thinking of average velocity over some finite time. This is not how instantaneous velocity is defined - it is defined as a limit when the time interval goes to zero. Speed is defined as the magnitude of instantaneous velocity. Simple as that.

Claiming something else is just wrong.

In the image below are depicted both, average velocity, by displacement $\vec{d_{1}}$ , and also instant velocity provided by displacement $\vec{d_{4}}$ .

You say that speed is the magnitude of velocity, which is correct only for instantaneous velocity, I get it, when the displacement from point G to point H is very small and is the same as the trajectory from G to H, which I explicitly explained in my first post that velocity = speed only when the trajectory is straight, which is the case here.
When we are referring to average velocity, speed is not velocity, because the curved path ACB is not the straight displacement AB. The English language provides this distinction between speed (scalar) and velocity (vector), so why don't you use it? By insisting on speaking about speed = velocity, you can only cause confusion, because then you have to explain further that this is only valid for instantaneous velocity. Velocity has a magnitude, but it is not speed, not in English.

In everyday usage, the terms “speed” and “velocity” are used interchangeably. In physics, however, they are distinct quantities. Speed is a scalar quantity and has only magnitude. Velocity, on the other hand, is a vector quantity and so has both magnitude and direction. This distinction becomes more apparent when we calculate average speed and velocity.

To illustrate the difference between average speed and average velocity, consider the following additional example. Imagine you are walking in a small rectangle. You walk three meters north, four meters east, three meters south, and another four meters west. The entire walk takes you 30 seconds. If you are calculating average speed, you would calculate the entire distance (3 + 4 + 3 + 4 = 14 meters) over the total time, 30 seconds. From this, you would get an average speed of 14/30 = 0.47 m/s. When calculating average velocity, however, you are looking at the displacement over time. Because you walked in a full rectangle and ended up exactly where you started, your displacement is 0 meters. Therefore, your average velocity, or displacement over time, would be 0 m/s.
https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/2:_Kinematics/2.2:_Speed_and_Velocity

Landau here, feel free to point out whatever you may consider necessary
https://archive.org/details/landau-and-lifshitz-physics-textbooks-series/Vol 1 - Landau, Lifshitz - Mechanics (3rd ed, 1976)/page/1/mode/2up?view=theater

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

@blue raven has been thread banned from replying in this thread because of misinformation, and the thread is reopened provisionally.

 

[Orodruin]

explained in my first post that velocity = speed only when the trajectory is straight, which is the case here.

This is wrong. Velocity is not equal to speed. It never happens because velocity is a vector and speed is a scalar - they cannot be equal to each other. Speed is defined as the magnitude of velocity.

When velocity is mentioned without any other qualifiers, what is being meant is the instantaneous velocity, not the average velocity.

Your path example is never straight as it has non-zero curvature everywhere. That you can approximate it by a straight line whose direction is the direction of velocity is s separate issue. Regardless, speed is the magnitude of velocity along the entire path.