Does distance divided by time give you a constant speed?

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guitareleven
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Re: Does distance divided by time give you a constant speed?

Post by guitareleven » Wed Mar 22, 2017 5:46 pm

glassynails wrote:... If I have to drive 100 miles in 1 hour and the first 1/2 hour I end up only going 20 miles I must've "averaged" 20mph. So in order to get to my 100 mile mark in 1/2 hour remaining I have to drive 160 mph. .
If you travel 20 miles in half an hour, your average speed is 40 miles an hour, not 20. But according to what you said, you only maintained that average for half an hour, which is why your distance traveled at that point is only 20 miles, and not 40. So, you are right about the rest of it; having traveled 20 of your intended 100 miles leaves you 80 to go; to accomplish that in half an hour, you would then, as you say, have to average 160 miles an hour for the rest of the trip.

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Denian Arcoleo
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Re: Does distance divided by time give you a constant speed?

Post by Denian Arcoleo » Wed Mar 22, 2017 7:47 pm

Glassy, you are really confusing me. You go from asking questions that no one knows the answer to, to questions that everyone over the age of seven knows the answer to and you appear equally puzzled by both. I don't get it.
(I remember attempting to explain the 3/4 6/8 relationship to you with little success and thinking, well, it ain't rocket science!)

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Re: Does distance divided by time give you a constant speed?

Post by glassynails » Fri Mar 24, 2017 11:02 pm

guitareleven wrote:
glassynails wrote:... If I have to drive 100 miles in 1 hour and the first 1/2 hour I end up only going 20 miles I must've "averaged" 20mph. So in order to get to my 100 mile mark in 1/2 hour remaining I have to drive 160 mph. .
If you travel 20 miles in half an hour, your average speed is 40 miles an hour, not 20. But according to what you said, you only maintained that average for half an hour, which is why your distance traveled at that point is only 20 miles, and not 40. So, you are right about the rest of it; having traveled 20 of your intended 100 miles leaves you 80 to go; to accomplish that in half an hour, you would then, as you say, have to average 160 miles an hour for the rest of the trip.
I meant I averaged 20 mph in the half hour.
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Re: Does distance divided by time give you a constant speed?

Post by glassynails » Fri Mar 24, 2017 11:08 pm

Denian Arcoleo wrote:Glassy, you are really confusing me. You go from asking questions that no one knows the answer to, to questions that everyone over the age of seven knows the answer to and you appear equally puzzled by both. I don't get it.
(I remember attempting to explain the 3/4 6/8 relationship to you with little success and thinking, well, it ain't rocket science!)
My example of going 20mph for a half hour and then 160 for the next half hour doesn't show a 'constant' speed. That's what I meant. If I travel 20 mph for the first half hour, I've gone 20 miles distance. Then I speed up to 160 mph for the next half hour and end up traveling 100 miles total. If I drove 100 miles in one hour people would assume that I must've traveled at 100 mph, which in this case is not true. So dividing distance by time does not give you a constant speed, it gives you an "average" speed.
"GLASSYNAILS" on Youtoob for my "no edit" - "no fakery" audio recordings. Just me, my Alhambra 7p spruce, and an Olympus ls-10 portable recorder.

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Re: Does distance divided by time give you a constant speed?

Post by gitgeezer » Sat Mar 25, 2017 1:03 am

When McGraw-Hill starts work on a new edition of its popular third-grade math text, you should send them this problem.

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guitareleven
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Re: Does distance divided by time give you a constant speed?

Post by guitareleven » Sat Mar 25, 2017 3:26 am

glassynails wrote:
guitareleven wrote:
glassynails wrote:... If I have to drive 100 miles in 1 hour and the first 1/2 hour I end up only going 20 miles I must've "averaged" 20mph. So in order to get to my 100 mile mark in 1/2 hour remaining I have to drive 160 mph. .
If you travel 20 miles in half an hour, your average speed is 40 miles an hour, not 20. But according to what you said, you only maintained that average for half an hour, which is why your distance traveled at that point is only 20 miles, and not 40. So, you are right about the rest of it; having traveled 20 of your intended 100 miles leaves you 80 to go; to accomplish that in half an hour, you would then, as you say, have to average 160 miles an hour for the rest of the trip.
I meant I averaged 20 mph in the half hour.

But you didn't. You averaged 40 mph. Had you maintained that average of 40 mph for an hour, as in"miles per hour" then you would have gone 40 miles. But , you maintained that average of 40 mph for only half an hour. Therefore, the distance you traveled, in that half hour of averaging 40 miles an hour, was half of 40, which, as you stated, was 20 miles. If you like, instead of stating it in terms of "mph", which is "miles per hour", then you can state it it in "mp½h", which is "miles per half hour". This is a non-standard measurement, but is just as accurate, and then, if that's what you want, you get to speak of your average as having been 20. You just have to clarify the departure from standard if what you also want is to be understood.

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Re: Does distance divided by time give you a constant speed?

Post by glassynails » Sat Mar 25, 2017 8:06 am

My point is that given a said distance one cannot tell what 'constant' speed someone is traveling at, but rather they can get an 'average' speed. If I travel 100 miles in one hour no one will be able to tell how fast my car was traveling at all times during that hour. I could drive really slow for the first half hour and end up going on 20 miles distance and then speed up to 160mph to go the remaining 80 miles in a half hour. You can never know a constant speed.
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bert
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Re: Does distance divided by time give you a constant speed?

Post by bert » Sat Mar 25, 2017 8:54 am

glassynails wrote:You can never know a constant speed.
Well, you can check your speedometer while using cruise control (although that probably is also an average speed with small intervals).
Last edited by bert on Sat Mar 25, 2017 11:26 am, edited 1 time in total.

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Re: Does distance divided by time give you a constant speed?

Post by joachim33 » Sat Mar 25, 2017 9:03 am

glassynails wrote: For example, If someone drove 100 miles in 1 hour we wouldn't have any idea what speed he was always traveling for that hour, just that he got there in 1 hour and drove 100 miles. So I'm now assuming that - distance / time = average speed.
It is average speed. If you want to dig into velocity (which is what scientists call speed) further, you need differential calculus, which is high school or 1st year University material. As you correctly figured the velocity depends on the time and knowing the average velocity does not give you the full picture.

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Re: Does distance divided by time give you a constant speed?

Post by Mr Kite » Sat Mar 25, 2017 11:00 am

glassynails wrote:If I travel 100 miles in one hour no one will be able to tell how fast my car was traveling at all times during that hour. I could drive really slow for the first half hour and end up going on 20 miles distance and then speed up to 160mph to go the remaining 80 miles in a half hour. You can never know a constant speed.
Seems you're on the way to discovering Heisenberg's uncertainty principle - you just need to consider what would happen if you measured the distance travelled more often during the journey.

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Re: Does distance divided by time give you a constant speed?

Post by glassynails » Sat Mar 25, 2017 7:17 pm

joachim33 wrote:
glassynails wrote: For example, If someone drove 100 miles in 1 hour we wouldn't have any idea what speed he was always traveling for that hour, just that he got there in 1 hour and drove 100 miles. So I'm now assuming that - distance / time = average speed.
It is average speed. If you want to dig into velocity (which is what scientists call speed) further, you need differential calculus, which is high school or 1st year University material. As you correctly figured the velocity depends on the time and knowing the average velocity does not give you the full picture.

Why insult with "high school" material? You cannot know what speed I was traveling at any given moment, that's my point! If I traveled 100 miles you have know way of determining my "constant" speed, because I can slow down and then make up time by going faster.
"GLASSYNAILS" on Youtoob for my "no edit" - "no fakery" audio recordings. Just me, my Alhambra 7p spruce, and an Olympus ls-10 portable recorder.

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joachim33
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Re: Does distance divided by time give you a constant speed?

Post by joachim33 » Sat Mar 25, 2017 10:24 pm

glassynails wrote: Why insult with "high school" material? You cannot know what speed I was traveling at any given moment, that's my point! If I traveled 100 miles you have know way of determining my "constant" speed, because I can slow down and then make up time by going faster.
No insult intended - sorry. We might have an issue with lost in translation, I was not educated in the US system. In the German system I attended 30 years ago, I got a glimpse of these concepts in Gymnasium and learned stuff properly in 1st year university Physics.

Have a nice evening.

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Re: Does distance divided by time give you a constant speed?

Post by rojarosguitar » Sat Mar 25, 2017 11:52 pm

glassynails wrote:As I was laying in bed last night trying to fall asleep I got to thinking about the old distance, time and speed equation and pictured myself having to drive 100 miles in a car (not that I do, but just for example).

So I thought of something like this: If I have to drive 100 miles in 1 hour and the first 1/2 hour I end up only going 20 miles I must've "averaged" 20mph. So in order to get to my 100 mile mark in 1/2 hour remaining I have to drive 160 mph.

So I had always taken it that distance / time = constant speed (mostly because I never think about these things much anymore), but I believe it actually means "average speed". Am I right?

For example, If someone drove 100 miles in 1 hour we wouldn't have any idea what speed he was always traveling for that hour, just that he got there in 1 hour and drove 100 miles. So I'm now assuming that - distance / time = average speed.
That's exactly it. Distance / duration = average speed. I deliberately say duration, because time is what you read on your watch. A famous mathematical theorem states that a continuous function of time must have at least one point of time when the actual value of that function is equal to that average value. Reversing that argument it follows, that your speed needs only one moment be equal to your average speed and well can be different from it all the other time!
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Re: Does distance divided by time give you a constant speed?

Post by gitgeezer » Sun Mar 26, 2017 2:16 am

Let's consider a coordinate plane with the y-axis representing speed and the x-axis representing time, with zero at the origin. If a vehicle begins accelerating at a constant rate of acceleration from zero, the acceleration line will be a straight line beginning at the origin and angling upward to the right, the steepness (slope) of the line being determined by the rate of acceleration, until it reaches some predetermined point of time (or until it reaches the time required to arrive at its destination. We're not concerned with what happens to the vehicle after that point--that's the driver's problem.)

The average speed will be determined by extending a straight horizontal line from the y-axis in such a way that it crosses the acceleration line at its mid point. The average speed will be the point at which this line meets the y-axis. (Some may be shocked to see that the average speed line shows a high rate of speed even at the point where the vehicle is only just starting its journey!) At the point where the two lines cross (at their mid-points), and at this point only, the speed of the vehicle will match its average speed.

What am I trying to demonstrate with all this? I have absolutely no idea.

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Re: Does distance divided by time give you a constant speed?

Post by fast eddie » Thu Jun 15, 2017 2:10 am

average speed.

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