Infinite acceleration?!

[Fluffz]

Originally posted by Verthanthi
Fluffz, if an object moves 1 meter in 1x(10^-5) s as you suggested, that would be an average velocity of 100000 m/s. 100000 m/s in less than a millisecond, is it any wonder you're receiving massive acceleration? It requires massive acceleration.

I'll admit I can't pin down what it is that you're fucking up, but it's there.

thats about the whole point. an infinite small way x will always be a lot of bigger than an infinite small time t² (1 doesnt stand for 1 meter just shows the relations of those two values)

i didnt quite get where you got that functions from but i think you are describing v~t and not a~v/t² a(t)=v'(t)? anyway...

been picked in base :/

[geekbot]

Re: Re: Infinite Acceleration

Originally posted by !cER
In the first instant an object moves from rest t=0, and it moves some distance (if it didnt move any didnt move any distance then the time wouldnt equal zero). Therefore the acceleration which is change is distance divided by change in time is a distance divided by zero which is infinite.

You guys are driving me crazy. !cER, this first instant that you are talking about does NOT happen in zero time. Nothing in the physical realm happens in zero time- that would be neither observable nor measurable. If you say that position (or velocity) changes in zero time then you are saying that something can be in 2 places at once. Clearly not possible.

Since nothing can be in 2 places at the same time, they must be in 2 places at two DIFFERENT times (even if these places and times are very close together).

Say the first instant an object moves from x=0 to x=x2 is at time t=t2. The previous instant (t=t1) it was at x=0. The non-zero, NON-INFINITE velocity is (x2-0)/(t2-t1) or x2/(t2-t1). The non-zero, NON-INFINITE acceleration is x2/(t2-t1)/(t2-t1).

[EternalEntropy]

Originally posted by Fluffz
no sir mr caps writer guy i doubt that since this function does not allow the time to be 0 without being an undefined devision by zero. because of this there cant be a point 0 on the graph since in no time u cant have gained any speed can u?

but the graph has to start somewhere and in this impossible tiny intervall u get an impossible high acceleration (speed / time²).

furthermore no matter how little the speed is the time² will always be smaller.

result: drastical raise of acceleration, and if u make the interval small enough... acceleration = -infinite/-infinite² = 1/-inf = inf

btw u cant draw that

It takes 2 points to measure acceleration, not 1. So you cant measure acceleration at a single point (0 in this case)

edit: I dont know why I bother telling you since you're like 10 years old and probably wont understand anyways.

[Fluffz]

Originally posted by EternalEntropy
It takes 2 points to measure acceleration, not 1. So you cant measure acceleration at a single point (0 in this case)

edit: I dont know why I bother telling you since you're like 10 years old and probably wont understand anyways.

yes u can thats all the poing of the d's in dx/dt². i doubt U graduated in anything yet or your schools are realy the suck

and geek than you have to invite a better formular. the one above allows having an acceleration in an dimensionless intervall

INFINITE no matter how much this is against your logic


maybe u get it the other way round. if u stop something, at the exact time of reducing the speed to 0 (which must exist or u'd never stop) it must also be infinite. it cant be 0 can it because then the speed would not have been reduced and it would still move. and if it would be any other number it would not be the point of the total stop since then, according to the formular, there would have to be a way x which isnt at the point of the stop. but it cant be 0 we had that and what is left? infinite yay i win gg
(this isnt realy correct since you can not realy describe the point of stop so easy with this formular but it schould give you the idea)


how hard go get is that ffs

[geekbot]

Originally posted by Fluffz
an acceleration in an dimensionless intervall

I don't understand what you mean. The inverval is whatever time interval is measured.

a = x2/(t2-t1)/(t2-t1)

dimension of a is distance/time/time (m/s/s or however you want to measure).

Time is non-zero because as I said before, you can't measure the position of something to be at x=x2 and x=x1 at the same time (only different times).

I'm sure you realize that math equations can only describe what we see in real life. They are only useful as long as they model real life close enough for your measurments/calculations.

Calculus is a mathmatical construct that can be used to solve things by closely approximating that thing. For example, you can solve for the area under a curve by approximating that area as a summation of rectangles. As the width of the rectangles approaches an infinitely small width, your approximation will become infinitely close to the actual area under the curve.

You wouldn't, however, say that that curve is actually a collection of rectangles with infinitely small width. Similarly, although change in velocity and change in acceleration can be appoximated by a summation of discrete positions or velocities over infinitely small steps of time, you can't really say that velocity or acceleration is actually changing over infinitely small delta time.

The approximation of infinitely small changes in time cannot be measured (does not exist) in real life.

[Troll King]

Just to clear up the idea for those who aren't quite sure about acceleration and havn't taken any calculus, and want to (pun intended) get up to speed:

people are looking at accelerations at a specific time. In other words, if you see a car at an intersection start moving when the light turns green, you can see that the car is accelerating, right? That means that at every single moment after the car starts moving until it reaches a cruising speed, it is accelerating. So imagine this accelerating car was captured on film. If you paused the film as the car was halfway through the intersection, the car is still accelerating at that particular moment.

[EternalEntropy]

Originally posted by Fluffz
yes u can thats all the poing of the d's in dx/dt². i doubt U graduated in anything yet or your schools are realy the suck

and geek than you have to invite a better formular. the one above allows having an acceleration in an dimensionless intervall

INFINITE no matter how much this is against your logic


maybe u get it the other way round. if u stop something, at the exact time of reducing the speed to 0 (which must exist or u'd never stop) it must also be infinite. it cant be 0 can it because then the speed would not have been reduced and it would still move. and if it would be any other number it would not be the point of the total stop since then, according to the formular, there would have to be a way x which isnt at the point of the stop. but it cant be 0 we had that and what is left? infinite yay i win gg
(this isnt realy correct since you can not realy describe the point of stop so easy with this formular but it schould give you the idea)


how hard go get is that ffs

for the record, you are an idiot.

Using your logic every time something is moving it would have infinite acceleration at all times. If I was measuring acceleration of a car at the start of a green light, it would have infinite acceleration at the very beginning. If someone was measuring the acceleration of the same car a second later, it would have infinite acceleration according to the other guy because his time on the graph would be 0 that second later.

To make it easier for you, imagine you graph the speed of a car who is sitting at rest for 5 seconds. The graph would show a straight line at y = 0, for 5 seconds. After that 5 seconds the car starts moving, you're saying that from 5 to some point after 5 seconds there is infinite acceleration? You need two points to measure acceleration based off a graph of the speed of the object over time. You are thinking acceleration is Velocity divided by time, when it is actually change in Velocity divided by change in time.

[Fluffz]

Originally posted by geekbot
Calculus is a mathmatical construct that can be used to solve things by closely approximating that thing. For example, you can solve for the area under a curve by approximating that area as a summation of rectangles. As the width of the rectangles approaches an infinitely small width, your approximation will become infinitely close to the actual area under the curve.

so far do good. you split the kurve in infinite tiny parts, add an infinite number of them together and get the effect of a delta. not very clever is it? so why do we use a d instead of a delta?
lets move from 1st grade physics to 6th grade maths.
to describe something you need 2 things.

a) a formula
b) values for that formula (input and output)

erm now at this point i am stuck because i sucked at maths. why the heck do i have to proove there is an infinite acceleration YOU proove me wrong the answer lies somewhere at the definition of the values and their borders.
like if you have an acceleration duration of 1 second: t € ]0,1] and for all those input values(one of them being 1/10^infinite) you get output values (one of them being infinite).
at this point delta t would be 1 but dt allows the full range of results

you can't really say that velocity or acceleration is actually changing over infinitely small delta time.

true or else you would have an infinite acceleration at all possible points but you can calculate the value at the beginning and at the end where to my poor knowledge you get the result of infinite. and this is what the topic is about. explain hot to reach infinite acceleration.

The approximation of infinitely small changes in time cannot be measured (does not exist) in real life.

acceleration is not a real life value. you cant measure or weight it. you gain a value trough a mathematical construct that describes the relation v~t. this construct isnt perfect (jet) so you can get strange results at some values. as i said you gotta invent a better formular if you are unhappy.

yet i might be wrong, the more i thing about the stranger it gets. i think Verthanthi is right and somewhere in there is a bug but i cant find it either. (like how can you add an infinite number of infinite values together and get an acceptable acceleration? i duno, maybe you cant say x is going slower to the 0point than t² or it is any other strange effect that dx can deliver. yes i think the problem lies in it being dx/dt² and not x/dt² but to work with that i think you have to study maths)

but wait, i see in the preview that troll is posting clever things. maybe you have an infinite acceleration at all points? like he said you are still accelerating even tho it passes no time

[Fluffz]

Originally posted by EternalEntropy
Using your logic every time something is moving it would have infinite acceleration at all times.

there is no to me known way how to calculate the dimensionless intervall at any other time then the beginning and the end

now go put your logic somewhere else and get some real maths fighting skills you FREAK

to clear things up i am not an idiot and maths is not what i usualy talk about

[EternalEntropy]

Originally posted by Fluffz
there is no to me known way how to calculate the dimensionless intervall at any other time then the beginning and the end

now go put your logic somewhere else and get some real maths fighting skills you FREAK

to clear things up i am not an idiot and maths is not what i usualy talk about

Why did you even bring up the topic of dimensions? That isnt relevant at all.l

I'll repeat three times for you, you need 2 points in time to MEASURE acceleration. Get it through your thick skull that there is no such thing as infinite acceleration. An object at infinite acceleration would travel anywhere instantly, though I wish in this instant I could acceleration my fist from where I am sitting into your face instantly, it isnt going to happen. An object that infinitely accelerates would experience no change in time from point a to point b because time isnt a constant value always. There is no real problem with the equation, take a graph of speed and find the change in time and change in speed and you will get acceleration and in *EVER* instance it will not be infinite. Go find me one instance where it is infinite acceleration and I will tell you why you are wrong.

[Mayo Inc.]

NERDS!!!!

jk, its interesting i just thought id lighten it up, whoa tough crowd

[Troll King]

Whoa, people are getting personal here. Let's take a step back and calm down.

Okay, now that's that's taken care of, let's break the problem down a bit. Let's give this scenario a chew. (And for once, it doesn't involve much calculus) It's a bit like what Verthanthi said earlier, but adapted a bit.

The people supporting the idea that there is an infinite acceleration do so based on the problem of instants. We are looking at an instant of time, giving us a delta t = 0. The problem at hand is that there is a conflict over this as well as how to properly assess acceleration with fewer than two instants.

Let us get around this problem then. Let the particular instant that we are looking at be known as Io. Since we have difficulty due to delta t being 0, let us then include two other instants, the one prior to Io (we'll call this one I1) and the one after Io (and we'll call this one I2).

This gives us I1 and I2 with Io sandwiched in between them.

Since I1 and I2 surround Io, we can find the difference in both velocity and time between these two instants, giving us delta v and delta t for Io.

These values will may seem infinitesimally small, but because of the definition of the setup, they are definately finite and non-zero. With these finite values for delta v and delta t, we can therefore calculate a finite value for the acceleration at Io.



There. How's that?

[Epinephrine]

Originally posted by Troll King
Whoa, people are getting personal here. Let's take a step back and calm down.

Okay, now that's that's taken care of, let's break the problem down a bit. Let's give this scenario a chew. (And for once, it doesn't involve much calculus) It's a bit like what Verthanthi said earlier, but adapted a bit.

The people supporting the idea that there is an infinite acceleration do so based on the problem of instants. We are looking at an instant of time, giving us a delta t = 0. The problem at hand is that there is a conflict over this as well as how to properly assess acceleration with fewer than two instants.

Let us get around this problem then. Let the particular instant that we are looking at be known as Io. Since we have difficulty due to delta t being 0, let us then include two other instants, the one prior to Io (we'll call this one I1) and the one after Io (and we'll call this one I2).

This gives us I1 and I2 with Io sandwiched in between them.

Since I1 and I2 surround Io, we can find the difference in both velocity and time between these two instants, giving us delta v and delta t for Io.

These values will may seem infinitesimally small, but because of the definition of the setup, they are definately finite and non-zero. With these finite values for delta v and delta t, we can therefore calculate a finite value for the acceleration at Io.



There. How's that?

Basically troll just did the delta-epsilon proof in his own way, the proof that shows you how calculus limits work, and thus will show why infinite acceleration does not exist.

-Epi

[Fluffz]

posted by Troll King
This gives us I1 and I2 with Io sandwiched in between them.

Since I1 and I2 surround Io, we can find the difference in both velocity and time between these two instants, giving us delta v and delta t for Io.

yes, no, problem! I1 and I2 are infinite close to 0 if i got that right. now delta would be I2-I1. the result of this is not a fine number but undefined just like the roof of -1. so you have no delta t and no acceleration
( small - small = ? ).

but you dont need 2 values one is enough. the problem could be down there when i use the rule of l'hospital without understanding it
lim x,t->0 (dx/dt²) = lim (1/2t) = infinite = limit value

furthermore you cant have the point of I1 just image something drives 10 seconds, 5 of them with a constant speed and 5 of them accelerating. a delta t of 10-4 gives an other result than a delta t of 10-5

posted by EternalEntropy
If someone was measuring the acceleration of the same car a second later, it would have infinite acceleration

additionally id like to say dont change the reference models or relation system(now idea how you call it) this will only make trouble. acceleration starts at t0 and x0 by definition. there is no acceleration before you increade v and if u change t0 to a random point and compare it to the former t0 you might get closer to solving this by throwing darts

posted by EternalEntropy
An object at infinite acceleration would travel anywhere instantly

no, acceleration is not speed. by adding the factor time to infinite acceleration the results is a speed of 2m/s or 10m/s or whatever

posted by Troll King
The people supporting the idea that there is an infinite acceleration

that people would be me and i have to go now for at least one week ill post more clever things when i am back

[Troll King]

Originally posted by Fluffz
yes, no, problem! I1 and I2 are infinite close to 0 if i got that right. now delta would be I2-I1. the result of this is not a fine number but undefined just like the roof of -1. so you have no delta t and no acceleration
( small - small = ? ).

You forgot one thing though: by definition, I1 and I2 are both distinct from Io. Therefore there must be a finite (though admittedly really small) difference between them. You assumed that the difference is so small that it is zero. That's a fallacy, as if it were zero, the three instants would occur at the exact same moment. That isn't the case becuase we defined I1 and I2 as events that occurred seperately from Io. Though delta t approaches zero and is really small, by definition it never actually reaches zero, so you cannot assume that it is.

Oh, and the square root of -1 is not undefined, but rather within the realm of imaginary numbers.