accereration 101

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>One else has inquired so I will-about acceleration being linked to time and velocity in some cases and not in others. acceleration is equal to velocity/time(a=v/t) or is this incorrect? How about when both velocity and acceleration are constant over any time period? How is this writen in math symbols?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Acceleration is independent of velocity. Any acceleration can go with any velocity. One way to measure a constant acceleration is to measure a velocity over some time interval, then divide the velocity by the time interval. But a better, more general definition is that acceleration is the rate of change of velocity. Whether velocity is big or small, its rate of change can be anything, at least for an instant.

An impulse is a sudden change in velocity. (Technically, it's a sudden change in momentum. But let's not get technical here.) It is modeled as an instantaneous change in velocity. A truly instantaneous change in velocity is logically impossible. But it is modeled that way because that is the simplest model when we don't know the details of the transition. An instantaneous change in velocity is an infinite acceleration by definition of acceleration: delta-V is finite and delta-t is zero. -|Tom|-

Ah Hah..., I think I've finally got what you are saying Dr. VanFlandern.

I think that what you are saying is that the acceleration can be any number because acceleration is not "velocity" but simply the "change" in velocity and the change is not a speed and therefore can be infinite, am I right?

In a different post( www.metaresearch.org/msgboard/topic.asp?TOPIC_ID=149 ) you gave me an example of a car with a maximum velocity of 60mph, and you said it could accelerate at 60 billion mph per sec. for a nanosecond. I then asked, "Isn't 60 billion mph per sec for a nanosecond the same as 60mph?"
You never answered.
I need to ask it again: How is your acceleration of 60B mph for 1 nanosec any different from a velocity of 60mph? They both travel the same amount of length in the exact same period of time.

I think I have it, I think you are saying that no matter what the length or the time that you can reduce both of them down "infinitely".
Example: I say the number is 1 and you say no, it's infinite and it's not a number, it's a "fraction" and I can reduce it down an infinite number of times see look:
1*1, 2*1/2, 4*1/4, 8*1/8, 16*1/16...infinity. The results of the fractions are no different from the original number 1. Wow, you can have an infinite number of fractions and they all equal 1, how is that any different from 1?

I might be a little dumb but I'm not stupid. It seems as though you are either confused about infinity or you are playing some kind of shell game. Perhaps it's just me, like I said, I-am-a-Dummy.

Just learning!
Magoo

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[Magoo]: I think that what you are saying is that the acceleration can be any number because acceleration is not "velocity" but simply the "change" in velocity and the change is not a speed and therefore can be infinite, am I right?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

A change in velocity is still a velocity. Acceleration is the <i>rate</i> of change of velocity. A rate is not a velocity.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>you gave me an example of a car with a maximum velocity of 60mph, and you said it could <u>accelerate</u> at 60 billion mph per sec. for a nanosecond. I then asked, "Isn't 60 billion mph per sec for a nanosecond the same as 60mph?" You never answered.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Too many people on the MB now. I can't keep up. Will do my best.

No, it isn't the same. However, because I set the parameters that way, the net change in velocity that comes out of the acceleration is the same, which I admit was confusing. So my example should have read [specially for your benefit] we can accelerate a car at 1 billion mph per second for a nanosecond, or 1 trillion mph for a picosecond, or at any acceleration for a short time. There is no connection to 60 mph, except that we were envisioning 60 mph as a "speed limit" that we will never exceed. I never exceeded it despite indefinitely large accelerations.

No shell games on this MB, Magoo. There's enough of that going on in science today. -|Tom|-

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>(Dr. VanFlandern)No, it isn't the same. However, because I set the parameters that way, the net change in velocity that comes out of the acceleration is the same, which I admit was confusing. So my example should have read [specially for your benefit] we can accelerate a car at 1 billion mph per second for a nanosecond, or 1 trillion mph for a picosecond, or at any acceleration for a short time. There is no connection to 60 mph, except that we were envisioning 60 mph as a "speed limit" that we will never exceed. I never exceeded it despite indefinitely large accelerations.

No shell games on this MB, Magoo. There's enough of that going on in science today. -|Tom|-<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Thank you for your response but I must challenge you here. With all of your credability at stake, by over exagerating your example in order to try and prove that acceleration cannot be infinite, can you <u>HONESTLY</u> tell me that you could accelerate at 100 Billion mph per sec for a picosecond [or for your sake a nanosecond] and not exceed the 60mph velocity? If your answer is "NO" then how could acceleration be infinite if velocity has a speed limit? How is this any different then the example I gave above and claimed "shell game"?<img src=icon_smile.gif border=0 align=middle>



Just learning!
Magoo

Come one guys! What's the story here, I fix cars all day long!

Newton's law guys: if something moves even for an instant at infinite acceleration simply means, from F=ma,the force on it, even for a picosecond, is infinite. God must be pushing it aint't right? Don't you tell me it ain't right I'll throw this physics book I have in the trash.

Even if it wasn't for Eistein and speeds could get infinite, accelerations wouldn't for the same season. You can start at 1m/s/s acceleration and in infinite time if such a thing exists you'll be speeding at an infinite speed. But friends, you cannot have infinite acceleration because according to the guy whp got the apple on his forehead such a thing requires infinite force, even for a picosecond. Only the ALL MIGHTY GOD can push that hard.

What's the story here I can't make it out. Who is talking about infinite accelerations?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>
[Magoo]
In a different post( www.metaresearch.org/msgboard/topic.asp?TOPIC_ID=149 ) you gave me an example of a car with a maximum velocity of 60mph, and you said it could accelerate at 60 billion mph per sec. for a nanosecond.

---

You and Dr Van Flandern seem to be dancing around the problem, so I'd like to take a stab at it...

Suppose 60 mi/hr is a "speed limit" of some sort.

Q) if you accelerate at 1 mi/hr/sec, how long will it take you to reach a speed of 44 mi/hr?
A) 44 sec (speed = accel * time)

Q) if you accelerate at 10 mi/hr/sec, how long will it take you to reach a speed of 44 mi/hr?
A) 4.4 sec (this is a typical real rate of acceleration for many real vehicles)

Q) if you accelerate at 100 mi/hr/sec, how long will it take you to reach a speed of 44 mi/hr?
A) 0.44 sec (440 millisec)

Q) if you accelerate at 10,000,000 mi/hr/sec, how long will it take you to reach a speed of 44 mi/hr?
A) 0.0000044 sec (4.4 microsec)

And so on. In the real world of physics you can pick any value (and, by definition, any <b>specific</b> value, no matter how large, is <b>finite</b>) for acceleration in this problem, and <b>as long as you make the appropriate adjustment to the time period during which that acceleration is applied</b> the answer will always be 44 mi/hr.

But in the make-believe world of mathematics, we can <b>pretend</b> that infinity is a number under some conditions and do calculations with it. Mathematically, this <b>impulse</b> occurs in zero time, implying an infinite acceleration. It is a handy tool for analysis, <b>but we do know that what happens in the real world is different</b>.

I used a target speed of 44 mi/hr instead of 60 mi/hr to explicitly demonstrate that the existance of a speed limit is not important in this problem (unless you exceed it, of course). As long as your speed <b>at the end of the period of acceleration</b> is less than the speed limit, you can accelerate as "hard" as you want.

We sometimes say "accelerate as fast as you want", but we shouldn't. The word fast is misleading when applied to the concept of acceleration.
<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>{Magoo}
I then asked, "Isn't 60 billion mph per sec for a nanosecond the same as 60mph?"<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>
Yes, it is. Do you understand why, now?

(acceleration is NOT speed, but acceleration times time IS).

Regards,
LB