inverse speed

[michel123456]

/i was traveling today and having nothing better to do I was thinking about speed.

Speed is represented by distance divided by time, meters divided by seconds: the amount of meters traveled in one second.

The reverse (inverse, opposite) would be the amount of seconds traveled in one meter. It is the amount of seconds needed to travel one meter. Which is still a speed.

Just as if the inverse of speed was speed. Or am I completely wrong?

[Strange]

Well, t/d is not speed it is inverse-speed (I don't think this unit has a name). There is no particular reason that the rate of movement couldn't be defined in those terms; I guess it is just less intuitive to have a unit that gets smaller the faster you go.

 

There is also the practical problem: what is the value of your inverse-speed when you are stationary?

[studiot]

Good points, strange. Particularly the last one. +1

Edited April 15, 2015 by studiot

[Acme]

...There is also the practical problem: what is the value of your inverse-speed when you are stationary?

It could be useful in ballistics to know how long it will take a projectile to reach the target, particularly if the target is moving.

[Strange]

It could be useful in ballistics to know how long it will take a projectile to reach the target, particularly if the target is moving.

 

Or for measuring who wins a race over a fixed distance ...

[Janus]

Or for measuring who wins a race over a fixed distance ...

As in running a 4 min mile or a 10 second 100m.

[swansont]

Fuse burn rates are in seconds per meter (or foot).

[pavelcherepan]

As in running a 4 min mile or a 10 second 100m.

 

Agreed. Most running apps by default display your pace in mins/km.

 

On the side note of inverse units I always found funny that in Imperial measurements fuel consumption is measured in miles/gallon, while in most other places it's liters/100km.

[Strange]

On the side note of inverse units I always found funny that in Imperial measurements fuel consumption is measured in miles/gallon, while in most other places it's liters/100km.

 

In the UK, that is pretty much the only place we still use gallons. Even the petrol is priced in pence per litre.

 

It still sounds odd when I hear Americans talk about buying a quart of milk. Would you like a bushel of cookies to go with that, to sustain you on your journey of several furlongs?

Edited April 16, 2015 by Strange

[studiot]

A quart of milk?

 

Don't you buy flagons?

 

Interestingly I grew up in a dual world UK education system.

Metric and Imperial.

 

When I first went to work at the end of the sixties, civil engineering had converted to nearly fully metric.

Cement came in hundredweight bags or metric tonnes.

Concrete was just being converted from cubic yard mixers to cubic metre mixers.

So concrete was ordered in multiples of 4.8 cubic metres.

 

So imagine my suprise when I went to work for the americans in the late seventies and found myself working in Imperial, for the first time.

 

Bigger suprise, the company was working in grads not degrees.

 

[Greg H.]

 

In the UK, that is pretty much the only place we still use gallons. Even the petrol is priced in pence per litre.

 

It still sounds odd when I hear Americans talk about buying a quart of milk. Would you like a bushel of cookies to go with that, to sustain you on your journey of several furlongs?

Back up the truck.

 

You have cookies? You planning to share those?

[Strange]

Back up the truck.

 

You have cookies? You planning to share those?

 

Sorry, sold out. Might have some more in a fortnight.

[Greg H.]

 

Sorry, sold out. Might have some more in a fortnight.

I'll make sure to have shillings on hand.

[Phi for All]

I'll make sure to have shillings on hand.

 

And you'll get your change in tuppence, so you don't have to feed the birds with your cookies.

[J.C.MacSwell]

 

And you'll get your change in tuppence, so you don't have to feed the birds with your cookies.

I started to laugh at that, but stopped as I was heading for the ceiling

[michel123456]

Well, t/d is not speed it is inverse-speed (I don't think this unit has a name). There is no particular reason that the rate of movement couldn't be defined in those terms;

Yes, exactly

 

I guess it is just less intuitive to have a unit that gets smaller the faster you go.

Why? It gets you less time to go somewhere.

 

There is also the practical problem: what is the value of your inverse-speed when you are stationary?

Well yes that is puzzling. If speed and "inverse speed" are 2 different representations of the same thing, there may be more than that.

 

-----------------

Second question

If I can express speed in m/s and in s/m, would it be allowed to mix the 2 systems in a same equation. For example when multiplying speed by speed, instead of obtaining speed squared, to obtain a unitless number.

Edited April 16, 2015 by michel123456

[Greg H.]

Second question

If I can express speed in m/s and in s/m, would it be allowed to mix the 2 systems in a same equation. For example when multiplying speed by speed, instead of obtaining speed squared, to obtain a unitless number.

 

There's no reason why not, but I expect the answer will be meaningless.

 

[latex]

\frac{16m}{1s} = \frac{1s}{16m}

[/latex]

 

Which just resolves to 1. Which makes sense, since you're measuring the exact same event.

[timo]

@Greg: I don't quite see how that equality holds. And also not what "resolves to one" means. You probably meant something that is correct but used an incorrect mathematical symbolism to represent it.

 

On topic, and from a more abstract point of view: If you have a property X and a known invertible function Y=f(X) over the domain of interest then Y holds the same information as X. Usefulness and ease of understanding then are the main reasons to chose one over the other - and the fact that 0 m/s is a velocity that is relevant in lots of applications may well be the reason for choosing this over seconds per meter (both are arguably similarly easy to understand). In everyday science, particularly in spoken conversations, this equivalence of information is very well understood and implicitly used all the time. It may be a bit less common in internet forums where nitpicking is considered a way to demonstrate knowledge about a subject.

Edited April 16, 2015 by timo

[Acme]

...It may be a bit less common in internet forums where nitpicking is considered a way to demonstrate knowledge about a subject.

Nice use of self reference! A pottle of ale for you.

[Greg H.]

@Greg: I don't quite see how that equality holds. And also not what "resolves to one" means. You probably meant something that is correct but used an incorrect mathematical symbolism to represent it.

I went back and reread the OPs question and realized I didn't understand it when I wrote my response.

 

His question has to do with multiplying the two together, not setting them equal to one another. I apologize.

[timo]

Nice use of self reference! A pottle of ale for you.

Looks like an excellent example of a unit of measurement that is very impractical. My limit is the Maß (https://en.wikipedia.org/wiki/Ma%C3%9F), and even that is a bit of a Bavarian freak idea.

[Acme]

Looks like an excellent example of a unit of measurement that is very impractical. My limit is the Maß (https://en.wikipedia.org/wiki/Maß), and even that is a bit of a Bavarian freak idea.

Actually, it's a very old measure based on doubling. Writing in Reading the Numbers, Mary Blocksma gives the following scale. The smallest measure is the ancient Egyptian Mouthful; presumably the Pharoh's mouth. Then:

2 Mouthfuls = a Jigger

2 Jiggers = a Jack

2 Jacks= a Jill

2 Jills = a cup

2 Cups = a Pint

2 Pints = a Quart

2 Quarts = a Pottle

2 Pottles = a Gallon

2 Gallons = a Peck

2 Pecks = a Pail

2 Pails = a Bushel

2 Bushels = a Strike

2 Strikes = a Coomb

2 Coombs = a Cask

2 Casks = a Barrel

2 Barrels = a Hogshead

2 Hogshead = a Pipe (other sources give the Butt as 2 Hogsheads)

2 Pipes = a Tun

 

PS Please forgive my pedantic digression.

Edited April 16, 2015 by Acme

[Endy0816]

You end up doing a comparison / finding a ratio between the two.

 

Twice as fast = 2:1 = 2 = 140km/h / (70km/h) = 140km/h * 1h/70km

[Acme]

/i was traveling today and having nothing better to do I was thinking about speed.

Speed is represented by distance divided by time, meters divided by seconds: the amount of meters traveled in one second.

The reverse (inverse, opposite) would be the amount of seconds traveled in one meter. It is the amount of seconds needed to travel one meter. Which is still a speed.

Just as if the inverse of speed was speed. Or am I completely wrong?

Where 'speed' is a measure of the rate of motion then yes, both representations are speed. The choice of which representation to apply depends on the circumstances of utility as the examples given demonstrate. Saying 'the inverse of speed is speed' is a semantic issue, not a mathematical one.

[Enthalpy]

Slowness exists in engineering practice, though I don't know its English name. It's used for wave propagation, especially in Surface Acoustic Wave devices (which use to be filters). Diagrams give for instance the material's slowness versus the direction, since it's easier to use further.