Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 313

Why zero velocity for zero displacement despite running round...

...the block at 5mph?

We’re told initially that velocity is speed, but with direction included in the measurement (that velocity is a vector quantity).

But then we’re told that velocity is the rate at which displacement occurs.

Which means if we run from our home to the park the velocity is >0 (so far so reasonable, for the novice student).

But if we run round the block, ending up back at our origin, the velocity is 0 (so far so confusing, for at least some novice students).

Q. When physicists agreed upon this (v=displacement/t) and it became standardized, did they do so having discovered a phenomenon about the world that was objectively true (v=displacement/t)? Or did they arbitrarily (not without good reason, of course, but arbitrarily in the sense that they could have framed it otherwise and it would still have worked) decide to frame things this way?

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Why zero velocity for zero displacement despite running round...

hi paulb203

Yes, it does seem crazy; you're not the first to think so.

Speed is said to be a scalar quantity. That means it has magnitude and nothing else. Velocity is a vector quantity. This means it has magnitude and direction.  For a 2D situation you could describe a velocity as 5mph in a direction NE or by giving two components, say, an Easterly component and a Northerly component [ 5(√2)/2 , 5(√2)/2 ]

It you went on a six stage journey around the sides of a hexagon always at 5 mph (the speed), your velocities could be:

[ -6/2 , 6√3/2 ] [ +6/2, 6√3/2 ] [ 6 , 0 ] [ +6/2 , -6√3/2 ] [ -6/2 , -6√3/2 ] and [ -6 , 0 ]

If you add those up to get the overall vector for the whole journey you get [ 0 , 0 ] and yet the total you have moved is 6 x side of the hexagon.

Average speed = 5                   average velocity = 0

It's a property of vector theory and it works, so mathematicians stick with it.

It works like this for displacement vectors too. If you throw a ball up and let it fall back to your hand then the total distance travelled is (height reached) x 2. But the vector displacement is zero because it is back where it started.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 313

Re: Why zero velocity for zero displacement despite running round...

Thanks, Bob.

"It's a property of vector theory and it works, so mathematicians stick with it."

Would you say that velocity has two different meanings.

One, it means speed in a particular direction.

Two, it means displacement / time.

---

Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Why zero velocity for zero displacement despite running round...

The displacement has to be a vector quantity; then these two are equivalent.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob