I have a question for the masses. if you were traveling at 60 mph

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Discussion Overview

The discussion revolves around a thought experiment involving a traveler reducing their speed as they approach a destination, questioning whether they would always be one hour away from it. The conversation touches on concepts related to motion, time, and mathematical reasoning, with references to paradoxes and the implications of speed changes on reaching a destination.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the scenario resembles Zeno's paradox, while others argue it does not.
  • One participant claims the original poster (OP) is correct in stating they would always be one hour away from the destination, but this is challenged by others who assert that this claim is conditional on maintaining speed.
  • Several participants discuss the implications of speed reduction, with one stating that the traveler would never reach their destination due to the infinite nature of the speed changes.
  • Another participant proposes that the speed changes occur only at mile markers, suggesting that the traveler does reach their destination after a full hour at the last mile.
  • Some participants introduce the concept of a convergent series to explain the situation mathematically, while others question the assumptions made about distance and time.
  • One participant argues that a human occupies a definite volume and space, suggesting that the time taken to cover distances increases significantly as speed decreases.
  • Another participant humorously remarks on the engineering perspective of measurement and distance, indicating a more practical approach to the problem.
  • There are discussions about the total time taken for the journey, with one participant estimating it to be around 4.68 hours.
  • Some participants express uncertainty about the implications of the thought experiment, with references to quantum physics and the nature of measurement.

Areas of Agreement / Disagreement

Participants express a range of views, with no consensus reached. Some agree with the OP's initial claim, while others contest it, leading to a debate over the implications of speed changes and the nature of reaching a destination.

Contextual Notes

Limitations include assumptions about speed changes occurring only at specific points and the implications of a human's physical size on the problem. The discussion also reflects varying interpretations of mathematical concepts related to motion and time.

trix5153
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I have a question for the masses.
if you were traveling at 60 mph and were 60 miles from your destination you would be 1 hour away from your point.

when you reached 59 miles away from your point you drop your speed to 59 mph. you are 1 hour away.

when your 1 mile from your point you drop your speed to 1 mile per hour. you are 1 hour away
... if you continue this for infinity you would always be 1 hour from your destination... I'm looking for some real help with this. is this correct?
 
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similar to zeno's paradox?
 


Ravalanche said:
similar to zeno's paradox?

No, this is NOT similar, really, to Zeno and the OP is correct that he would always be 1 hr from destination.
 


phinds said:
...the OP is correct that he would always be 1 hr from destination.
No.

He can only claim to be "one hour away" from his destination under the proviso that he were to remain at the current speed for the rest of the journey.

He won't. It is not true that he is "an hour from his destination".

Yes, he is reducing his speed the closer he gets. He will never reach his destination. In fact, if we consider his change of rate of speed, we can confidently say "he is infinitely far (in duration) away from his destination" at all points.
 


DaveC426913 said:
No.

He can only claim to be "one hour away" from his destination under the proviso that he were to remain at the current speed for the rest of the journey.

He won't. It is not true that he is "an hour from his destination".

Yes, he is reducing his speed the closer he gets. He will never reach his destination. In fact, if we consider his change of rate of speed, we can confidently say "he is infinitely far (in duration) away from his destination" at all points.

DOH you're right, obviously
 


Thank you all for your posts. I'm sorry for my ignorance, I thought of this when i was 16 and have never asked the question to some "SMART" people before. Is there a name for this? or is it just a know point in the community that this is true? Thanks again.
 


trix5153 said:
Thank you all for your posts. I'm sorry for my ignorance,..

Never apologize for not knowing something or for asking. A curious mind is a most treasured thing, especially around here.

trix5153 said:
Is there a name for this?

It is a convergent series.

An infinite series of numbers can add up to a finite number.

1/2 + 1/4 + 1/8 + 1/16 + 1/32 +1/64 + ... = 1
 
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Actually, since he's changing his speed in 1mph steps, he will get there unless he changes his formulation...

He's approximating a hyperbolic approach, but only approximating.
 


Sorry you will never arrive at your destination.

Figure out how far you go in each 1 min interval, sum them up. You will have traveled 30.5 miles when your speed reachs 0.
 
  • #10


As the question is posed he does reach his destination, because the speed change only occurs at the mile markers. So at the last mile, 1 mile from home he slows to 1mile and hour. An hour later he arrives at his destination and changes his speed to 0mph.
 
  • #11


tony_physic said:
As the question is posed he does reach his destination, because the speed change only occurs at the mile markers. So at the last mile, 1 mile from home he slows to 1mile and hour. An hour later he arrives at his destination and changes his speed to 0mph.
This sounds right to me. At each mile marker he's dropping his speed by 1 mph.

What that means is only that each mile takes progressively more time to cover, with the last mile taking a full hour.

Is there a quick way to add up the times and find out how long the trip takes doing it this way? I'm curious.

Working backward:

Mile 60 = 1 hr
Mile 59 = 1/2 hr
Mile 58 = 1/3 hr
Mile 57 = 1/4 hr
Mile 56 = 1/5 hr
Mile 55 = 1/6 hr
Mile 54 = 1/7 hr &etc

It's clear the bulk of the added time comes at the end of the trip and does not threaten to approach an infinite amount of time, or anything like that. Still, I'd expect the total time it takes to do it this way to be interesting in some way, shape, or form.
 
  • #12


You are all wrong in your reasoning, a human is not some infinitely small point, he/she occupies a definite volume and space. Take it from the last mile, or 1760 yds, which is covered in 1 hour. Then going on decreasing the distance the time increases , 2 hrs for the half mile, 4 hours for the quarter mile and so on. Until finally when he reaches the last yard (0.8593 yds to be exact) he takes 2048 hours or 85.3 days to cross that small distance. The point being that he does make it, even if it takes a long time!
 
  • #13


zoobyshoe said:
Is there a quick way to add up the times and find out how long the trip takes doing it this way? I'm curious.
I've got about 4.68 hours. Wolfram Alpha can do it in no time.
 
  • #14


nasu said:
I've got about 4.68 hours. Wolfram Alpha can do it in no time.
Thanks, nasu!

Well, that figure isn't as interesting as I'd hoped it would be.
 
  • #15


I have the answer for you. It is not a black or white answer and will surely piss off all those who like simple answers.

For the same reason that Schrödinger's cat is both dead and alive - a very real consideration in quantum physics, in your puzzle, the answer is that you will arrive at the destination eventually; however, it will take forever.
 
  • #16


McQueen said:
You are all wrong in your reasoning, a human is not some infinitely small point, he/she occupies a definite volume and space. Take it from the last mile, or 1760 yds, which is covered in 1 hour. Then going on decreasing the distance the time increases , 2 hrs for the half mile, 4 hours for the quarter mile and so on. Until finally when he reaches the last yard (0.8593 yds to be exact) he takes 2048 hours or 85.3 days to cross that small distance. The point being that he does make it, even if it takes a long time!
Why did you stop at one yard? Why do you all along assume he's halving the distance and halving the speed, and then when it gets down to a yard, you declare he just magically leaps across that distance?

As for a human being a non-zero size, this is not relevant unless you get sloppy with your measurements. When he started his journey, his toe (or bumper) had not crossed the starting line, and he's not done until that toe (or bumper) crosses the finish line. This is true whether he is a point, a person, a car or a whale. The point of measurement is indeed a zero-dimensional point.

Talk about being "wrong in reasoning". You did it twice in one paragraph. :biggrin:
 
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  • #17


It is up to the Engineers amongst us to say those immortal words "Near enough for Jazz". If you can't measure the separation distance then you've arrived.
 
  • #18


sophiecentaur said:
It is up to the Engineers amongst us to say those immortal words "Near enough for Jazz". If you can't measure the separation distance then you've arrived.

Agreed. If this were an Engineering Forum. But it ain't. :biggrin: We eat zero-dimensional points for breakfast.
 
  • #19


DaveC426913 said:
Agreed. If this were an Engineering Forum. But it ain't. :biggrin: We eat zero-dimensional points for breakfast.

Indigestion for the rest of the day?
:wink:
 
  • #20


Eventually the object would come to a movement so slow it wouldn't even matter.
 
  • #21


16 years old said:
...it wouldn't even matter.
A physicist will look at you like to just sprouted antennae.


Imagine a physicist saying...

"Well, we use a microscope to look at smaller and smaller things until we get down to these atom-thingies. That's small enough. Anything smaller doesn't really matter does it?"

:biggrin:
 

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