Is velocity ever a scalar quantity?

paulb203 · 2024-12-26 23:04:44

I thought velocity was always a vector quantity, one with both magnitude and direction.

When it came to suvat equations, where v = final velocity, and u = initial velocity, I thought both of those were vector quantities, e.g;

v (final velocity) 112km/hr North

u (initial velocity) 0km/hr (what do we put for direction when the object is initially stationary?)

But in a Khan Academy question they ask what does the letter v (lower case with no arrow above it, or anything else) stand for, and whether it’s a vector or a scalar.

I answered ‘velocity’ (it was multiple choice with no option for ‘final velocity’) and that it was a vector.

Their answer was;

“The symbol v represents speed, a scalar.”

I know speed is a scalar, but thought v stood for final velocity. I also know that final velocity IS speed, but thought that we had to include direction given the velocity part.

Bob · 2024-12-27 00:34:09

You say 'initial' and 'final' so I'm assuming you're using v = u + at.

I think v and u here are vectors. It's what I was taught .... velocity a vector, speed a scalar. But I tried google. The first 17 hits all had v as a vector. None as a scalar.

Strictly there should be some indication such as an overline or bold print,

but nobody seems to bother. But I guess that's why Khan thinks scalar.

In practice it'll come out in the calculation, so don't worry too much about the distinction.

Bob

Phrzby Phil · 2024-12-27 04:57:14

A bit sloppy for Khan (or anyone professing to be knowledgeable in this area) to use "velocity" as anything other than a vector.

In common everyday usage, I understand, but not professionally.

That having been said, why don't we call our steering wheel an "accelerator" when we're turning?

And why do we continue to call our gas pedal an accelerator once we have achieved a constant speed?

paulb203 · 2024-12-29 00:06:16

Thanks, Bob, thanks, Phil.

Having asked around I think I’ve got it now, and realise I should’ve included more information, and therefore context, with my question.

Khan was quite thorough with their notation. They showed various symbols and asked what each stands for and whether it was a vector or a scalar.
When they put x (for position) they had the little rightwards arrow above it, indicating a vector.
They also had an arrowed v, also indicating a vector.
And then they had a plain, unarrowed v, indicating, I think I see now, in this context, a scalar. Although someone pointed out that, strictly speaking, there should be vertical bars either side of this unarrowed v, to indicate absolute value, to indicate the magnitude alone of the velocity vector.

I’ve noticed in lots of maths questions (GCSE level) they keep it simple, e.g, no bar line above to indicate average rather than instantaneous; or no avg to indicate average; no arrows to indicate vectors; etc. I guess this makes sense given the context. It’s maths, not physics, even though it technically it is physics, if you know what I mean. And those letters (v, s, u, etc) could be any letters when the exercise is, for example, to show that you can change the subject of a formula.

Good points about the steering wheel and gas pedal, Phil

landonjameson · 2025-02-13 15:34:15

To denote the magnitude of the velocity vector, it is common to write it as ∣v∣∣v∣ (with vertical bars). This indicates the absolute value or magnitude of the velocity vector, ignoring its direction.

ktesla39 · 2025-02-14 01:43:59

Yup!
I never noticed in my school about these things until I was taught about vectors. You guys are right. v should have an arrow above it when it refers to velocity and just v while it's speed as velociy is speed in particular direction.

paulb203 · 2025-02-14 22:42:50

Thanks, guys.

paulb203 · 2025-02-14 22:50:51

@Phrzby Phil

“And why do we continue to call our gas pedal an accelerator once we have achieved a constant speed?”

Ah, you might be able to help me with a related physics question.
Once we’ve achieved a constant speed, and therefore we are no longer accelerating (assuming straight line travel), do we only need to keep our foot on the gas pedal to overcome friction? If there was no friction, could we take our foot off the gas and still maintain constant speed?
Also, once we’ve achieved constant speed is there no longer an unbalanced force on the vehicle?
I was initially thinking that the applied force would still be greater than the friction force and therefore the force would be unbalanced (with the gravitational force and the normal force cancelling each other out).

Bob · 2025-02-15 05:46:51

You could call it a throttle as that's how it works.

Once you've reached cruising speed there is still a force trying to slow you up made from wind resistance and friction so you still need to input some gas to create a force to overcome these.

Once there are no externally impressed force's Newton says we keep going at constant velocity.

Bob

paulb203 · 2025-02-16 22:59:07

Thanks, Bob.
It seems strange, to me, that an object in motion would remain in motion forever unless acted on by an unbalanced force, a kind of perpetual motion. Yet at the same time I’m thinking, ‘Why wouldn’t it? Why would there be any change to the situation without any ‘input’?’ And how did anything come to be in motion in the first place?

Bob · 2025-02-17 02:08:43

There's not much chance of observing uniform motion without external forces here on Earth chiefly because of friction and to a lesser extent air resistance.

In space it's happening all the time. The space craft that were shot off to escape the solar system are just continuing in the direction they were going when the fuel ran out.

And any object in orbit just keeps going. There is an external force; gravity; and that's what causes the orbit but .for example the Earth's tangential speed doesn't change significantly .

You could think about examples where the friction is very low such as in ice skating.

Bob

Echo_23 · 2025-02-18 21:11:20

paulb203 wrote:

I thought velocity was always a vector quantity, one with both magnitude and direction.
When it came to suvat equations, where v = final velocity, and u = initial velocity, I thought both of those were vector quantities, e.g;
v (final velocity) 112km/hr North
u (initial velocity) 0km/hr (what do we put for direction when the object is initially stationary?)
But in a Khan Academy question they ask what does the letter v (lower case with no arrow above it, or anything else) stand for, and whether it’s a vector or a scalar.
I answered ‘velocity’ (it was multiple choice with no option for ‘final velocity’) and that it was a vector.
Their answer was;
“The symbol v represents speed, a scalar.”
I know speed is a scalar, but thought v stood for final velocity. I also know that final velocity IS speed, but thought that we had to include direction given the velocity part.

You're absolutely right that velocity is a vector quantity, meaning it has both magnitude and direction. In the context of SUVAT equations, v typically represents final velocity, which is indeed a vector. The initial velocity, u, is also a vector, and if an object starts from rest, we usually assume its velocity is 0 m/s in the direction it will eventually move.

Echo_23 · 2025-02-18 21:13:00

paulb203 wrote:

I thought velocity was always a vector quantity, one with both magnitude and direction.
When it came to suvat equations, where v = final velocity, and u = initial velocity, I thought both of those were vector quantities, e.g;
v (final velocity) 112km/hr North
u (initial velocity) 0km/hr (what do we put for direction when the object is initially stationary?)
But in a Khan Academy question they ask what does the letter v (lower case with no arrow above it, or anything else) stand for, and whether it’s a vector or a scalar.
I answered ‘velocity’ (it was multiple choice with no option for ‘final velocity’) and that it was a vector.
Their answer was;
“The symbol v represents speed, a scalar.”
I know speed is a scalar, but thought v stood for final velocity. I also know that final velocity IS speed, but thought that we had to include direction given the velocity part.

The confusion likely comes from how Khan Academy framed the question. Sometimes, in general physics problems, v can refer to speed (the magnitude of velocity) if direction is not relevant. However, in SUVAT equations, it's normally understood as velocity. Their wording might have been trying to emphasize that v without an arrow can sometimes mean just speed, but in kinematics, you were correct to associate it with velocity.

phrontister · 2025-02-19 10:25:42

Echo_23's last post (#13) appends a paragraph that doesn't appear in paulb203's post #1...

Last edited by phrontister (2025-02-19 14:38:57)

Bob · 2025-02-19 20:19:08

Thanks phrontister, well spotted. If I see a post that is pure advertising I remove it and the new member/guest. This one wasn't selling anythng (I think) so I've edited it out but left Echo_23 as a member for now. It can get tricky when the 'offender' has put in actual mathematical content as I don't want to fragment the thread.

Any ideas on the dinner party post?

https://www.mathisfunforum.com/viewtopic.php?id=32566

Bob

Math Is Fun Forum

#1 2024-12-26 23:04:44

Is velocity ever a scalar quantity?

#2 2024-12-27 00:34:09

Re: Is velocity ever a scalar quantity?

#3 2024-12-27 04:57:14

Re: Is velocity ever a scalar quantity?

#4 2024-12-29 00:06:16

Re: Is velocity ever a scalar quantity?

#5 2025-02-13 15:34:15

Re: Is velocity ever a scalar quantity?

#6 2025-02-14 01:43:59

Re: Is velocity ever a scalar quantity?

#7 2025-02-14 22:42:50

Re: Is velocity ever a scalar quantity?

#8 2025-02-14 22:50:51

Re: Is velocity ever a scalar quantity?

#9 2025-02-15 05:46:51

Re: Is velocity ever a scalar quantity?

#10 2025-02-16 22:59:07

Re: Is velocity ever a scalar quantity?

#11 2025-02-17 02:08:43

Re: Is velocity ever a scalar quantity?

#12 2025-02-18 21:11:20

Re: Is velocity ever a scalar quantity?

#13 2025-02-18 21:13:00

Re: Is velocity ever a scalar quantity?

#14 2025-02-19 10:25:42

Re: Is velocity ever a scalar quantity?

#15 2025-02-19 20:19:08

Re: Is velocity ever a scalar quantity?

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