The Two Car Paradox
Discussion
What with all this time and relativity/expanding stuff flying about, let me reveal the secret of the Two Car Paradox.
Envisage two cars proceding one after the other along a road. The gap between them remains constant.
When I was a small boy I confounded my parents by insisting that the first car had to be travelling faster than the second car in order to stay in front. I thought that if they travelled at the same speed, they would end up side by side.
Normal physics says this is wrong, and that both cars are travelling at the same speed. So I just wondered whether, if one threw in some advanced Gene Vincent stuff, whether we could prove my childhood idea correct? Was I a child genius (now lapsed) or just plain wrong in any time and dimension?
Envisage two cars proceding one after the other along a road. The gap between them remains constant.
When I was a small boy I confounded my parents by insisting that the first car had to be travelling faster than the second car in order to stay in front. I thought that if they travelled at the same speed, they would end up side by side.
Normal physics says this is wrong, and that both cars are travelling at the same speed. So I just wondered whether, if one threw in some advanced Gene Vincent stuff, whether we could prove my childhood idea correct? Was I a child genius (now lapsed) or just plain wrong in any time and dimension?
Awwww man... it appears that you need more speed because the car in front accelerates before the one behind does out of every bend, the result is the impression that the car behind appears to need to go faster to keep up on Englands winding roads.
OK, I've solved that for you... now, have you any f
king idea whatsoever what the lottery numbers are tonight?
Tit-for-tat and all that!
OK, I've solved that for you... now, have you any f
king idea whatsoever what the lottery numbers are tonight?Tit-for-tat and all that!
Edited by Gene Vincent on Saturday 25th August 18:13
Simpo Two said:
Envisage two cars proceding one after the other along a road. The gap between them remains constant.
When I was a small boy I confounded my parents by insisting that the first car had to be travelling faster than the second car in order to stay in front. I thought that if they travelled at the same speed, they would end up side by side.
Why? How did you reach that conclusion?When I was a small boy I confounded my parents by insisting that the first car had to be travelling faster than the second car in order to stay in front. I thought that if they travelled at the same speed, they would end up side by side.
Surely the gap would remain constant, it seems pretty obvious to me, unless I'm missing something....
For the distance to remain the same they must both be travelling at the same speed as speed = distance/time so distance = speed*time. However, the car in front may be expending more work done to stay in front by virtue of punching a hole through the air assuming all other factors are the same i.e. car type, weight etc... Depending on the distance between the cars.
Gene Vincent said:
Awwww man... it appears that you need more speed because the car in front accelerates before the one behind does out of every bend, the result is the impression that the car behind appears to need to go faster to keep up on Englands winding roads.
OK, I've solved that for you... now, have you any fking idea whatsoever what the lottery numbers are tonight?
Tit-for-tat and all that!
I was rather hoping that the first car created a slight warping of the gravity field, such that when measured relative to itself it was going faster than the second car (gravity/time/speed yada), but wasn't from a bystander's view.OK, I've solved that for you... now, have you any f
king idea whatsoever what the lottery numbers are tonight?Tit-for-tat and all that!
I'll let somebody else do the proof as my maths expired at trigonometry level. Sorry no idea on the lottery; I avoid it as it's designed to raise money for somebody else, ergo I will lose it.
Ha ha, I've often be bamboozled by something very similair but with 3 cars...
So say your in the middle lane of the motorway doing 60, you've just overtaken someone on the inside lane doing 50 and someone is overtakig you on the outside lane doing 70, right?
Is there a point at which both cars are equidistant from you? It would seem their obviously is if the timing is correct but if the timing and speeds are random teh only truth being that the outside lane is always faster than the middle and the middle always faster than the left lane.
Is it true that there is always a point that the cars are equidistant and how do we express this mathematically?
Cheers.
P.S If this is gibberish please don't be rude.
So say your in the middle lane of the motorway doing 60, you've just overtaken someone on the inside lane doing 50 and someone is overtakig you on the outside lane doing 70, right?
Is there a point at which both cars are equidistant from you? It would seem their obviously is if the timing is correct but if the timing and speeds are random teh only truth being that the outside lane is always faster than the middle and the middle always faster than the left lane.
Is it true that there is always a point that the cars are equidistant and how do we express this mathematically?
Cheers.
P.S If this is gibberish please don't be rude.
Simpo Two said:
If you start the test when all three cars are abreast then, since the relative speeds are +10 and -10, I'd say they're always equidistant.
Yes, well spotted, so now slow the slow one and speed up the fast one, will they ever be equidistant? It seems not but how do I show this mathemaically. I think this stems from a maths lecture I missed or was sleeping through explaining integration and rate of change, when I see cars in lines of three it half comes back to me.Damn I won't sleep tonight.
mattnunn said:
Yes, well spotted, so now slow the slow one and speed up the fast one, will they ever be equidistant?
+20 and -20 makes equidistant in my book. They can be equidistant all the time, it just depends on their relative speeds and that includes accelerataion/retardation. But of course if one car accelerates slowly while the other one stamps on the brakes, the model fails.Hit the buffers on calculus, I much prefer graph paper
I don't think there's any paradox, just an equation which may or may not have a valid solution
If at time t=0
The distance between you and the slower car is d,
The difference in speed between you and the slower car is v,
The distance between you and the faster car is D,
The difference in speed between you and the faster car is V
Then at time T, you are d+vT from the slower car and D+VT from the faster car.
For equal distance, d+vT=D+VT.
If d=D and v=V then you'll always be the same distance regardless of T.
Otherwise, solve for T and if that gives T>=0 then yes there will be a point where they are equidistant, you can get the distance from plugging the value of T back into either formula.
Or I may have misunderstood the question
If at time t=0
The distance between you and the slower car is d,
The difference in speed between you and the slower car is v,
The distance between you and the faster car is D,
The difference in speed between you and the faster car is V
Then at time T, you are d+vT from the slower car and D+VT from the faster car.
For equal distance, d+vT=D+VT.
If d=D and v=V then you'll always be the same distance regardless of T.
Otherwise, solve for T and if that gives T>=0 then yes there will be a point where they are equidistant, you can get the distance from plugging the value of T back into either formula.
Or I may have misunderstood the question
Expanding (Heisenberg's ) Uncertainty Principle from the sub-atomic to the world we recognise, then if you know how fast the car in front is going you won't know where it is, or if you know where it is you won't know how fast it is going,
you're childhood feelings of assuming that despite apparently travelling at the same speed behind a car you would at some stage be level with it are perfectly reasonable in the sub- atomic world
You don't own a cat,( possibly dead ) do you ?
you're childhood feelings of assuming that despite apparently travelling at the same speed behind a car you would at some stage be level with it are perfectly reasonable in the sub- atomic world
You don't own a cat,( possibly dead ) do you ?
Pobolycwm said:
Expanding (Heisenberg's ) Uncertainty Principle from the sub-atomic to the world we recognise, then if you know how fast the car in front is going you won't know where it is, or if you know where it is you won't know how fast it is going,
you're childhood feelings of assuming that despite apparently travelling at the same speed behind a car you would at some stage be level with it are perfectly reasonable in the sub- atomic world
Best answer yet!you're childhood feelings of assuming that despite apparently travelling at the same speed behind a car you would at some stage be level with it are perfectly reasonable in the sub- atomic world
Pobolycwm said:
You don't own a cat,( possibly dead ) do you ?
I do own a cat, but am presently uncertain of its situation regardling life/death. However, it was most certainly alive at the vets this afternoon as it swiped him and he had to get a plaster!Elderly said:
Simpo Two said:
When I was a small boy .....
When I was a small boy, I thought that if a car was running out of petrolit should be driven faster in order to get to the petrol station sooner
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