Speed vs. velocity (from a "Jeopardy!" clue)

[Asympotically_fat]

@John_Mace

Maybe part of the OP’s problem is that, in English, speed and velocity are unique. No other vector has an explicitly different term for its scalar equivalent.

Other vectors:

Momentum
Acceleration
Force

It’s a good point that it rare for there to be a an explicitly different term for a vector and its magnitude, but the are (a few others): “distance” and “position”; “rest mass” and “four-momentum” in special relativity (depending on how you define magnitude); for example.

[Chronos]

And then there’s also “pickup”, which isn’t (in general) the magnitude of acceleration, but is instead the derivative of speed. Though I’ll grant that it isn’t often used.

[friedo]

@BigT

I assumed the point would be that it would break down if you had 2 dimensional velocity rather than one dimensional with a modifier. If the velocity is 3+4i, the term absolute value (3+4i) isn’t going to tell you the magnitude. You’ll need the Pythagorean theorem to find the magnitude is 5.

|a+bi| is conventionally taken to mean the magnitude of the vector, but is typically called the “modulus” rather than the “absolute value.”

This is why the correct way to teach absolute values is “distance from zero” rather than “flip the sign if it’s negative.” When you get the complex numbers, it’s still “distance from zero.”

[Pasta]

@Chronos

And then there’s also “pickup”, which isn’t (in general) the magnitude of acceleration, but is instead the derivative of speed. Though I’ll grant that it isn’t often used.

Where have you seen this used?

[John_Mace]

@Asympotically_fat

It’s a good point that it rare for there to be a an explicitly different term for a vector and its magnitude, but the are (a few others): “distance” and “position”; “rest mass” and “four-momentum” in special relativity (depending on how you define magnitude); for example.

Good point. But I don’t think most people think of “distance” and “position” as being the same in the sense that they think of speed and velocity. And most people don’t think about rest mass or four-momentum at all.

[Chronos]

Quoth Pasta:
Where have you seen this used?

Usually in the context of cars. Like, a car with a short 0-60 time might be said to have “good pickup”.

[Pasta]

@Chronos

Usually in the context of cars. Like, a car with a short 0-60 time might be said to have “good pickup”.

Oh, you mean that “pickup”. I might argue that it’s putting a bit too fine a point on that colloquial usage to say “pickup := d(speed)/dt”. Certainly if I applied the brakes, one wouldn’t say I had negative pickup.

[GoodOmens]

@Enola_Straight

I once came across a science textbook which claimed speed is the absolute value of velocity.

I take it some velocities have negative values.

Yes, because when defining velocity, one direction is defined (in some cases arbitrarily) as positive. If we think about vertical movement, for example, it’s common to define up as positive, so something which is falling would then have negative velocity, but positive speed.

Of course we could just as easily define downward as being the positive direction (if a bit confusing at first), so an object falling would then have positive velocity and a rocket during liftoff would have negative velocity.

That tends to blow my students’ minds. They have a lot of trouble with the fact that it’s perfectly OK to define down and left as positive if they want to; those a traditional choices but there’s nothing mathematically special about them.