Avant Brown Want to Play a Game?
Donating = Loving
Bringing you atheist articles and building active godless communities takes hundreds of hours and resources each month. If you find any joy or stimulation at Atheist Republic, please consider becoming a Supporting Member with a recurring monthly donation of your choosing, between a cup of tea and a good dinner.
Log in or create an account to join the discussions on the Atheist Republic forums.
Don't try to visualize the solution. Just work it out with the method you suggested earlier. It will give you the answer eventually.
This fear of starting a problem that you can't visualize the ending of before you start; is a serious problem I've discovered many students suffer from. Just get your hands dirty and see where the math takes you. Sometimes I call this "mathematical courage". 99% of the stuff I work on, I can't see the solution from the beginning. It is nice when you can do it, but it is not a requirement; acting as if it is a requirement will cause you big problems if you pursue this kind of work.
That's excellent advice.
But my worry here, is that the notation you gave namely "(2t^3 + t^2 + 5t +8)ĵ", although resembling a valid position, does not really seem to be a valid position. According to the books I've come across, which is only a few admittedly and other resources like the enotes on acceleration calculation, 2d positions tend to include unit vector pairs at minimum, including something like i and j.
I don't see any position that falls short of this cardinality of unit vectors any where else so far. So I am not confident in progressing, as I don't think it's legal to differentiate what resembles a position, but what really isn't one, as far as I'm seeing online. As far as I've seen there are rules for differentiation herein; measurements of change are occurring wrt important units like the vectors described.
It is a position function. It tells you the position o̶f̶ at every point in time:
Clearly it is a position function. You can also see here why the shortcut works, because the particle never changes position in the î direction.
In the initial problem you gave on page 1, you asked for the "î component of acceleration" of the position. What exactly are you asking for? It sounds like the coefficient of i after one would have differentiated a position to attain some velocity, then differentiated again to get the acceleration, then the acceleration/answer would look like this: 82î + 23j (as seen here), from which one would take 82 to be the answer to your question, if " î component of acceleration" is to be interpreted as the "coefficient of î".
If that's the case how would we get the coefficient of î if it is missing? Or did you mean something else by asking for the "î component of acceleration"?
Yes that is exactly what I'm asking for. I've already explained this, but I'll try again: the fact that î is "missing" from the position function, means its coefficient is 0.
Are you starting to see how easy this problem really is for someone familiar with the subject? And what a nightmare it is for people who are not? That is by design as well:
The problem is phrased in terms of position functions, acceleration functions, orthonormal unit vectors, and calculus. However I could have phrased it l like this: how much "up" motion (or acceleration) is there in a object that is NOT moving up? Then everyone knows the answer is 0. I wanted to see if the "PhD candidate" knew what the words meant; clearly he does not.
I'm thinking that the way you just phrased it, seems like an entirely different question altogether.
You asked for the "î component of acceleration", which seems to imply by default, that an acceleration would have already been calculated, and hence why the "î component of acceleration" or "î coefficient" was asked for. (Which would imply that unit vector i should have been in the position, from what I understand?)
Can you point me to any resource that shows what happens if the î component is missing? I don't mean an example question, I simply mean the mathematical implication of having the î component omitted?
Why did you multiply j by i above?
What rule gets you from the item you proposed as a valid position, namely: ""(2t^3 + t^2 + 5t +8)ĵ"" to multiplying j by i?
Vectors are not multiplied like scalars (the multiplication that most people know how to do is only for scalars), I took the dot product. Which tells us the magnitude in the î direction, of a vector in the ĵ direction; which is 0.
In imprecise English: I calculated how much "East" is in an arrow that points "North"; which is 0.
What I'm wondering really, is given your position ""(2t^3 + t^2 + 5t +8)ĵ", if the actual position is "(2t^3 + t^2 + 5t +8)ĵ ± (undefined-value-associated with i)", where i is omitted, how would we attempt to calculate the derivative "d/dt" of an undefined value, in order to identify the "i component of acceleration" from an acceleration calculation as you requested?
AGAIN: the position function could be written as (2t^3 + t^2 + 5t +8)ĵ + 0î + 0k̂; but the simplest way to write it is how I wrote it in the problem. The coefficient of an unlisted object is always 0; not undefined as you suggested.
Another simple way to explain it might be:
If I asked a person how many pets they have they might respond:
But that is equivalent to:
The lesson is: unlisted objects have a coefficient of 0. They are 0 because they don't contribute anything and can therefore be safely omitted.
Holy crap, dude, even I can understand that. And the most I have ever had is Pre-Cal. Hate to say it, but this Miss Stare is starting to sound a bit fishy, just as you mentioned a bit earlier in this thread. And if I am wrong, Miss Stare, then I do sincerely apologize. However, something ain't addin' up here. (Pardon the pun.)
Alright, I guess it's time to make things clear.
Note: Forgive me for some of the all-caps below, it's just used to emphasize some key points, to describe the huge issue I see with the problem you proposed on page 1, if I am not mistaken.
In simpler words, unlike dealing with coefficients in maths, the dimensions we are dealing with wrt your problem are not arbitrary, where you can simply invoke unstipulated items to exist as zero valued items, as you suggested above.
Math is my worst subject and I barely passed algebra, but wouldn't the y axis of anything 1D always be 0 because that axis wouldn't be represented?
Stare is starting to sound less and less like a fourteen year old girl with each post.
Everyone is a 14 year old girl online lol
@Random Re: "Everyone is a 14 year old girl online lol"
Not true. I'm only 13 and a half.
Not at all, as far as physics/motion calculations seems to go. The y-dimension would have to be specified to exist in the problem, or be given in the problem.
In math without any physics-like considerations, we can arbitrarily define coefficients to exist as zero-valued items, even if the associated variable is not stipulated, because they don't refer to specific structures with distinct properties.
However, from what I can see of physics or motion calculations, the math becomes specific; i.e. the quantities associated with the unit vector labels, like î, are very specific values, that describe very specific regimes. This means in the absence of labels, like î, we can't just assume that such an î based dimension exists in the problem, since it was not stipulated.
In simpler words, we can't just presume the y dimension exists in our particular problem space. Y=0 implies that dimension exists. Y not specified at all, implies the dimension doesn't exist at all in that space. Notably, 0 is not equal to being undefined.
I gave a link in my previous response about coefficients in math and physics: https://whatis.techtarget.com/definition/coefficient
A little garbled, but yes, that is correct.
This recent post of yours contains a large number of false claims, not questions.
Recently you repeatedly suggested assigning a scalar value to a vector, this is a neophyte mistake, the mistake of someone who doesn't really know what a vector is. Someone who is need of instruction (if they actually want to learn the subject). I'm more than willing to help provide some.
What I'm not willing to do is argue the finer points of vector and vector spaces with a neophyte. If that is what you are here for, you are wasting everyone's time.
I set up the 1st derivative for you to solve, but I see you haven't even attempted it yet. There is no 2nd orthonormal vector in that part of the problem, so your misguided complains don't even apply there. Are you planning on trying? It's OK to get it wrong, I'll walk you though any mistake. But you aren't going to learn anything if you don't try.
If you want me to review those false statements, I will; but I'd like to get some sign from you that you want to learn, not troll.
Which post are you talking about, where I made a neophyte mistake? This is possible since I really am a newbie here, but I can't find the mistake you refer to.
The only post I could find about related to scalars, is where I asked if i should be equal to 1 other dimension. I don't see how that makes it seems that I would think i to be a scalar.
Could you please explain why that would sound like I'm talking about scalars? (Ps, I know what vectors are, there just collections of numbers. A vector can almost look like a scalar, with "one entry" or 1 item. )
Yes, I did agree to him, but with one extremely crucial condition, 1D suggests that a y dimension exists unless I am mistaken.
I don't see anywhere so far in physics literature, where one can unspecifiy a dimension in a problem, then simply presume said problem includes other dimensions.
This means to me, that if Meepwned proposed a problem with 1D being on an x axis, there would be no reason to presume his proposed problem also included a y axis as well. Please correct me if I'm wrong.
Please correct me if I'm wrong.
Ps: Differentiations to begin, are very simple, it just takes one from the power of a variable, before which one would have multiplied the coefficient etc. I didn't differentiate the term for a simple reason, what you asked for didn't seem to agree with the dimension of your position.
As far as I understand, your position is 1D namely associated with "ĵ", but you asked for an item related to another dimension, namely associated with "î".
Is it legitimate to introduce a new dimension to your position, in order to try to solve what you asked for as I worried about in the recent post of mine you linked?
How many dimensions does your position refer to? Does what you ask for "the î component of acceleration" refer to a 2nd dimension that was not stated in your problem position? Do you agree that the position you gave was 1D as seen in these examples?
In simpler words, should I have ignored the difference between 1D and 2D kinematics, where what you asked for seems to concern 2D, while the position you gave was 1D?
I think the answers to these questions could clear up my confusion. Thanks.
Yes, that is exactly right, which means the answer depends on the "relationship" between ĵ and î; which is ĵ ∙ î; which depends on cos(π/2); which is 0.
You have gone back to the same disease, you seem unwilling to do any work on the problem because you can't see the finish line; even though you agree this first step is easy. Finish (or at least try) the first step I gave you.
You have a lot of false assumptions about working with dimensions. You need to abandon them if you want to learn anything. It is a very common trick to express motion in the standard basis (î, ĵ, k̂) as one dimensional motion. It is one of the first things you will learn how to do in an introductory physics class because it greatly reduces the difficulty of a problem.
Hold on, no where did I say one can't work with a 3D motion concerning X dimensions, in terms of a 1D motion concerning X-n, that is, if you start with a 3D motion, depending on the task, one can "constrain", but still stipulate some dimensions such that the initial 3D structure "looks like" a 1D structure.
However, your question didn't start at X dimensions, it started at X-n dimensions namely 1D, so structures involving 2D would not be there to support a scenario, where we can benefit from shared vector space found in 2D structure, from what I can see.
Please correct me if I'm wrong.
Differentiating your position does not yield any i term, which is related to what your problem asks for; from what I can see differentiation in this regard does not yield new dimensions.
Can we benefit from shared vector space operations, between j and a supposed i, when i was unspecified to begin with?
Do you want to troll or learn? Last chance. Don't blow it.
I wish to learn.
Crucial question: I know that one can observe relationships between vectors in shared vector space, for eg, between two unit vector data in 2D i.e. between i and j or k and i for eg.
However, can we still benefit from that type of relationship, if we start with 1D? Is there anything for dimension 1 unit vector to relate to, if there's not shared space between two sets of unit vector, i.e. only 1D exists in problem? Is going from 1D to 2D not a separate physics question altogether?
Then calculate the velocity function (or at least attempt it) in your next post.
The answers to your questions will become obvious if you do the work. If you continue to try to troll by just stringing together random mathematical terms you have googled, you won't learn shit.
You know, I am glad I ain't got to work on mathematical equations anymore. Except maybe for some algebraic rearrangement. I just know how to find them, use them, and program them into a script/program. Mostly that is what I do. I just program the equations in with appropriate text boxes to enter the variables, then let the program solve it for me. To hell with plugging it into a calculator. Give me a program where I can enter the variables and hit <Enter> to calculate.