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

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?

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