Wednesday, February 06, 2008

Rate Of Speed

Have you ever heard of people using the phrase "rate of speed" before? I have, mainly on TV during one of our local news. Usually it is during a description of some vehicular traffic incident, and some vehicle was described as moving at a "high rate of speed". What they really want to say is simply that the vehicle was moving very fast, but somehow, they think saying "high rate of speed" sounds "sexier".

This, of course, is rather inaccurate. Typically, when say say "rate of something", we usually mean the time rate of change. In calculus, it is d/dt of something, i.e. the time derivative. So when one say "rate of speed", one is actually saying ds/dt, where s is speed. This is ACCELERATION!

Now there's nothing wrong with this if the newscasters actually did intended to say acceleration (which begs the question on why they don't just say "acceleration"?). But more likely, they wanted to say "speed". So really, transposing "speed" into "rate of speed" is not only non-economical in terms of words to say, it is also no longer correct.

So, if you write for some news broadcast, and you want to say that a vehicle moves very fast, just say "high speed" and NOT "high rate of speed". If your producer or proof reader disagree, ask him/her to open a physics textbook.



Matt said...

In my country, at least (the UK), there's a saying "high rate of knots" (meaning high speed) which presumably comes from the old naval method of measuring speed. That's reasonable because that's explicitly saying a 'high rate of displacement'. This 'high rate of speed' is either a malaprop based on that, or just someone trying to sound intelligent. And it really annoys me too!

I support your campaign :)

Augie Physics said...

TV news and sports are full of science and math mistakes. My favorite was the football announcer who had been told that power was force times distance over time. "And does this guy have power," he said. "He has a lot of force times a big distance over a long time." Groan.

I'm not sure what rate of speed means. It is certainly "non-economical in terms of words to say," but I don't know that it means acceleration either. That would be rate of CHANGE of speed (or, rather, velocity). I think it is as matt said, "just someone trying to sound intelligent," and missing the mark.

Sam said...

So, the as far as I can tell, the sports announcer is correct. work is force times distance, and power is work over time, so P=(force*distance)/time

Anyway, I agree. Rate of speed is ambiguous and sounds kind of silly to those who actually know a thing or two about physics.

Anonymous said...

Sam... that comment didn't make sense. You don't call work, rate of distance times force? Rate of speed is the wrong term unless your talking about acceleration.

Anonymous said...

I actually arrived at this post by googling "high rate of speed" because I wanted to know if I was the only one for whom this is so irritating. Glad to know I'm not alone!! Keep fighting the good fight!

Tom in Greenbelt said...

It's not that this "begs" the question so much as raises a question. But I guess "begging a question" sounds "sexier" ;-)

Anonymous said...

A large force over a large distance over a LARGE time will not necessarily give you a large power ouput.

Time is in the denominator, so a smaller time will increase power.

The newscaster should have said "a large force over a large distance over a short time".

A different Sam said...

It is ambiguous to say "rate of speed", but not for the reasons you suggest. "rate of speed" could not mean acceleration, because a) acceleration is the derivative of velocity, not speed (vector, not scalar) and b) a derivative of something isn't its rate, it is its "rate of change". "Rate" can only apply to a process, ie "rate of growth" or "rate of reproduction" or "rate of change", since "change" is a process. Saying "rate of speed" makes no more sense than "rate of size".

ZapperZ said...

OK, now you're nitpicking more than I would.

First of all, have you ever heard TV newscasters using the word "velocity", other than referring to the title of a movie? So what they mean by "speed" is velocity, mainly because these are usually in reference to some linear motion of a vehicle.

Secondly, the term "rate" as used a normal context of such discussion is d/dt, i.e. the TIME rate of change. Don't believe me? Look at your "interest rate"!


The same different Sam said...

I actually don't really care if they say "rate of speed", but if you are going to nitpick, you might as well go the full way :)

Have I ever heard newscaster use the word velocity? Not that I can remember, but the physics of it is usually right; most of the time they say speed they actually do mean speed. But acceleration is not the derivative of speed.

Secondly, no, not quite. When we say "rate of change" in physics we mean "rate of change with respect to time"; that's fine (if we don't want the time derivative, we say so). But we can't say "rate of speed". Interest rate is a special case; I'm pretty sure many dictionaries will have it under a separate definition of rate. I don't think you can say "rate of X" with a non-process noun for "X", with the exception of "rate of interest" (not sure you can even say that). Interest rate is a rate (%/year, usually), but its not really a "rate of interest", its a "rate of paying interest".

I wouldn't nitpick this much for a newscast, but since you are calling your blog Physics and Physicists...

J said...

This phrase has bothered me too hence I found your page. The term "rate" in math simply means with respect to time. I can understand how the term "rate of speed" would bug a physics person but this is largely semantics at play. It could be argued both ways. The term "speed" is a rate in itself. So referring to a speed value as "rate" is not really wrong, just redundant.

In any case, it's usually a police officer on television who wants to sound intelligent who's saying these things. Some other "sexy" redundant phrases these closet English majors use are "red in color" and "at that particular point in time".

Another engineering related one that bugs me is "full throttle". A phrase that literally means the opposite of it's popular definition, wide open throttle.

cjp3iii said...

Speed is rate of change of distance. So, when someone says, rate of speed, they are saying rate of rate of change of distance. I do think this is acceleration?

eyeammi said...

Technically, with regards to calculus, for that expression to equal acceleration, you would have to say, "the time rate of change in speed." "Rate of speed" is a correct way (albeit slightly redundant) of expressing the change in distance per unit time. The "of" in this case is equivalent to specifying what kind of rate you are talking about.

It's like saying, "a shade of red." All colors are a kind of shade, but this specific shade is red. All rates are a ratios of one quantity to another but this kind of rate is speed.

ZapperZ said...

Then you just contradicted yourself. By saying "rate of speed" is the same as "change in distance per unit time", you have already indicated that this should be said as "rate of displacement".

In calculus, regardless of whether it is specified over what quantity the change is, a "rate of something" is equal to


A time rate of change of something is then


This STILL is not the value of that something. It is the change of that something with respect to some quantity.

If rate of speed is the same as speed, then that's saying 2 = 1. Rate of speed is NOT speed.


eyeammi said...

No, I didn't contradict myself because that's not what I said. I said that acceleration is the same things as "the time rate of change in speed." "Of," in this case, is understood by replacing it with, "specified by"

A rate in calculus is a change is something with respect to a change in something else:

(d(something)/d(something else).

The "the time rate of change in distance" is equavalent to saying:

the rate of [the change in distance with respect to the change in time]

or equivalently:

the rate of [d(distance)/d(time)]

Speed = d(distance)/d(time) = []

Therefore "rate of speed" or "rate specified by speed" is the exact same thing as saying, "time rate of change in distance"

Rate is made specific by refering to speed which is a kind of rate.

This is equivalent in structure and usage as the following:

shade of red
sound of music
state of Washington
nation of Italy
feeling of joy
crop of corn
sport of soccer
art of painting
talent of juggling
game of chess
rate of speed

All these phrases can be understood by recognizing that they are really saying that, for example, the type of game is specified by the word chess.

The type of rate is specified by the word "speed" which is itself defined by d(distance)/d(time) which is a kind of rate.

ZapperZ said...

No, I disagree that that list is equivalent to "rate of speed". Shade of red, for example, simply indicates that "red" comes in different shades. It is neither redundant, nor does it change the meaning.

But why are you invoking linguistic when we are dealing with the mathematical/physical definition of the word? You were the one who invoked "in calculus".

The "rate" of something implies the CHANGE of that something with respect to a quantity. Now, do you have a problem with that definition based on physics/mathematics?


eyeammi said...

A rate = [change in something/change in something else] It doesn't "imply" change, it's defined by change.

However, a rate is not just the change in something or just the change in the something else. you cant seperate the "something" from the "something else." Otherwise the concept of a rate has no physical meaning.

You are trying to make it read like:

{Rate of the change in distance} with respect to time.

That is not correct. In the context of what a rate physically means, it is correct to read it as:

Rate OF [the change in distance with respect to time]


The rate GIVEN BY [the change in distance with respect to time] where [] = SPEED.

ZapperZ said...

You read it wrong. I said that a rate is the change of a variable with respect to a quantity, i.e. dy/dx. Speed is ds/dt.

So a rate of speed is d(speed)/d(something). In this context, it is d(speed)/dt, which is acceleration.

At the end of your comment, you even said that speed is change in distance with respect to time. This is time rate of displacement! It isn't time rate of speed!


eyeammi said...

We both agree that:

Given any continuous quantity, x & any other continuous quantity, y, a kind of rate can be defined as:

rate = dy/dx (or dx/dy for that matter)

a rate ≠ dy & rate ≠ dx

if y = s ≡ distance & x = t ≡ time


dy/dx = d(distance)/d(time) ≡ speed


rate = dy/dx = d(distance)/d(time) = speed


the rate equal to (the change in distance with respect to time)...

What does rate equal to? The rate equals to (Speed)!

the rate of (the change in distance with respect to time)...

What kind of rate? The rate of (Speed)!


the rate of (the change in speed with respect to time)...

What does rate equal to? The Acceleration!

Acceleration and Speed are both kinds of rates. and for a quantity to be a rate, such as speed, the change in something is inseparable from the change in something else. You cannot define a rate without expressing the change in two related quantities. If you see only one quantity, as in, "the rate of (speed)", it is because the two changing quantities have be substituted by the single quantity they both jointly define.

ZapperZ said...

Oy freaking vey!


eyeammi said...

My Yiddish is a little rusty, but I believe that, "Oy freaking vey" loosely translates to, "I'm trying to hide under the guise of exasperation from the fact that I was wrong all along and had to have something so simple explicitly spelled out for me by a random guy on the internet."

On second thought, I may have taken a few liberties with that translation.


ZapperZ said...

Oh brother! You give yourself way too much credit!

I decided to cut this off because I'll be repeating the SAME thing. It appears that you're here only to argue.

In physics, it is unusual for something to have two different "names". Speed is speed, and rate of speed is rate of speed. To argue that

speed = rate of speed

is like saying 2 = 1

You seem to agree that, at the very least, "rate of x" means the change in x. I go a step further in saying that it is "change in x with respect to a quantity". EITHER WAY, both of those definitions are NOT equivalent to "x", i.e. rate of x is not equal to x. If they are equal, there is no need to invent a new mathematical/physical expression.

As a commenter earlier on has mentioned, it is certainly a "non-economical" term that, as has been shown here, can induce a confusion of meaning! At the very least, THAT in itself should be ample reason to not use such a term. If you mean speed, say speed! If you mean high speed, say high speed!

Again, there is nothing new in what I've said here, and we seem to be going around in circles. Unless there's something new and profound, I'm cutting off this argument right here. We can choose to both disagree on this, and I believe I've given you enough air time to voice your disagreement.


Michael said...

Compare and contrast with "Rate of acceleration". You often see/hear people say "rate of acceleration". Even a quick search on google books shows that the phrase crops up in several technical books.

Does anybody think that "rate of acceleration" is synonymous with "rate of change in acceleration"? I'm sure most people will agree that "rate of acceleration" means something along the lines of "measure of acceleration".

I would therefore argue that "rate of x" simply means "measure of x". "change" is a possible value of x and so is "acceleration". Why isn't "speed"?

Grammatically it seems reasonable. Technically, I see no reason to treat it different to acceleration.

It can only be aesthetics.

ZapperZ said...

I'm sorry, but you are essentially claiming that the phrase "rate of speed" is the same as just saying "speed". Maybe it is the "same" in the pedantic, pedestrian language. I don't know. If it is, no wonder politics is so screwed up, because we call can define things differently, and different words can mean the same thing.


Step said...

RATE: some thing with respect to time.
Ex: Rate of reaction(Reaction change with respect to time)
Displacement rate(displacement with respect to time)
at time t1=0sec, point p at the distance d1=0cm from a fixed reference point,
at time t2=2sec, point p at distance d2=2cm
Displacement rate= displacement/total time
Position change gives displacement displacement per unit time give seed or velocity.If speed or velocity changes with respect to time gives acceleration.
" SPEED RATE or rate of speed:How speed changes with respect to time"
If Rate of speed=0 that means speed is constant
Rate of displacement=Velocity or speed.(position changes with respect to time)
Rate of speed=Acceleration.(speed changes with respect to time)

** am i right?**

Anonymous said...

I can understand the English (but not physics) usage of "rate of speed" just like the more commonly used phrase "rate of acceleration". In these cases, the word "rate" implies a property -- "speed, which has a property of having a d/dt" and "acceleration, which has a property of having a d/dt". This is common in other English uses like "shade of red", which is "red, which has a shade property (light red, dark red, etc.)"

What bugs me a lot is the placement of the modifier "high". A "high rate of speed" changes the "rate" from being a property to a modifier itself. In essence, the phrase becomes "high d/dt of speed", or high acceleration. It should be written as "rate of high speed", interpreted as "a high speed, which has a d/dt property". This is in line with usages like "state of Washington politics" instead of "Washington state of politics".

There are cases where both seem to work -- "Southern area of Italy" or "area of Southern Italy" (though I'd argue for some kind of standardization there too), but that is only because the modifier "Southern" does not change the interpretation of the word "area". In our case, it does.

The usage of the word "rate" is redundant and needs to be removed, given that "having a d/dt property" is directly implied by the word "speed" or "acceleration", and to save STEM people from fuming every time they come across one of these.

- An engineering graduate student's take

James CRAFTON said...

I appreciate how you describe how rate of speed is inaccurate. I also appreciate how you then go on to use the phrase begs the question incorrectly.

ZapperZ said...

Thank you! It's good to be appreciated!

Unfortunately, I have no idea what point you are trying to make here? If this is a blog about the proper use of the English language, then I suppose I should be ashamed, embarrassed, and maybe even feel so devastated as to either throw myself off a cliff or hide myself from the rest of civilization for as long as I live. Maybe that's what you were hoping.

Luckily, it isn't, and if that is the ONLY thing you could fault me in that blog entry that I made, then I can only hope you'll realize how PETTY your comment was. So sorry that you had wasted your time for nothing.


Jason M said...

This phrase bugs me too.

While I understand 'color of red' type of analogy, with at best, 'color of' being redundant.

Although 'rate' is already implying a change with respect to time. Like 'rate of displacement'.

At best it's redundant, at worst it's nonsensical, so it's best just to drop 'rate of speed'.

As for the 'begs the question' it's pointing out the logical fallacy. 'Begs the question' has a very specific meaning and doesn't mean 'leads to the question.' Begging the question refers to a type of circular reasoning not what's slowly creeping into common usage, not unlike rate of speed.

Quiz Dog said...

I learned in sailing class that "rate of knots" would once have been dimensionally correct usage because the speed of a ship used to be measured by throwing out the end of the rope that had knots tied into it at fixed intervals.

Counting the number of knots that went by as the rope was pulled out by the ship moving through the water over a fixed period of time gave the rate of knots which was dimensionally length / time (or speed)

Of course since then knot has evolved to mean one nautical mile / hour
so "rate of knots" is back to being length / time / time with the same dimensional issue as "rate of speed"

Heretic? said...

I googled "first written occurrence of 'high rate of speed'" and found a number of Journals's from 1875-1892 (and probably later) dealing with "Commercial Education" in general and Stenography, and Phonetics in particular that used the phrase "high rate of speed" in reference to the rate at which one could take shorthand dictation. Pitman in London, UK, may have been the "authoritative source" which was copied by the other tomes, however he also was probably merely reflecting common usage then.

As stenographers, those folks were probably NOT well versed in physics. "Speed" is indeed the rate of some occurrence over time, whether words per minute or miles or kilometers per hour, and saying "a high speed" is free of confusion. "Speed" is the same type of word as "Wage", which is a "rate of pay", and "Knots" which is "nautical miles per hour" (and is a specific example of a speed).

"Rate of Speed" isn't the only example of popularly spoken redundancies. My mother likes to jump on "these ones" and she is correct that to say simply "these" out to be sufficient.

The police commonly use the phrase because, as in the case in the Province of Ontario in Canada, it is used in the Highway Traffic Act when discussing driving at in excess of the speed limit. It is an unfortunate fact that lawyers, who revel in multiplying words through repetition and the use of tautologies, make every officer look like a uneducated boob by having put that awkward phrase in legislation.m

voxleo said...

Well let's examine it practically by separating the definition of words from the definition of physics terms. There is a context which demands that words mean something in casual conversation that is readily referenced by the common folks, not just the nerdy folks who delight in over-analysis like ourselves having this discussion. While vocabulary does overlap, we cannot switch the contexts of reference without breaking the function of communication. Rules must be applied consistently to make sense. Altering the context of the vocabulary is a logical fallacy that breaks those rules of consistency.

In terms of language comprehension alone, clarity comes from the posts which recognize the word "rate" as a "measure(ment)" and that in order to measure something, it must be contrasted with something else. The root demonstrates that RATe is a RATio.

Speed, by definition, is a measure of motion in a ratio of time and distance, irrespective of direction of motion. Velocity is a measure of both speed AND direction, and acceleration is a measure of change in velocity (either speed OR direction). Acceleration, like speed, is itself a rate, a measure.

Linguistically then, it would make no sense to mean acceleration (which is a measure of CHANGE, not a measure of a measure) with the phrase "rate of speed" because that would not signify the change in speed or direction, only the MEASURE of it. It is inflexibly a bad linguistic choice to mean acceleration OR speed because it really means "a measure of a measure of motion in terms of time and distance".

The essential argument for it being the same as acceleration as a physics term is inherent in the understanding that you would have to DO the measuring to define that change, but that's also changing the functional context of communication in using that as a meaning or reference as a scientific definition. Then, as with the expression "e=mc^2", you are turning the words of the sentence into a symbolic representation of process, a scientific shorthand expression of concept, as opposed to using the words as concrete definitions - as words meaning what they represent as words alone.

Although it must be measured to calculate acceleration, it is not appropriate to equate measure with change you are measuring in that manner. It is a bit absurd to try and force that context on it anyway because that would require some flexible defining of acceleration for the sole purpose of making that linguistic choice inflexible. It is ineffectively pedantic linguistically, and false equivalence logically.

voxleo said...

To say "rate of speed" is simply redundant. It is less akin to saying "a shade of red" than it is to saying "as black as black."

As noted, the proof is in the modifying descriptive word "high" being applied to the word "rate", which only makes sense if you use it to mean a ratio of distance/time (ie "speed" which has the same definition in both scientific and linguistic understanding). A "high rate" is a "high ratio". Ergo, it is correct to say "travelling at high speed." In this case the ratio is SPEED (aka - the ratio of time to distance). It becomes gobbledygook when you mean it to be a rate (ie "measure") of that ratio, because the measure IS the ratio.

If you really must use the word "rate" then you could discuss a rate of MOTION or TRAVEL and still be correct, but a rate of speed is a "rate of ratio" which makes no proper sense in physical science, mathematics, OR English at all. Trying to assert that the linguistic understanding of the phrase could translate into a scientific definition of acceleration sort of requires the same brand of semantic double-talk that causes it to be redundant, but sort of working in the other direction requiring any vagueness be filled in with a specific assumption of meaning that it doesn't inherently have.

Not only would that involve poor application of language in communication, it would also be poor application of science in drawing conclusions.