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I want to know the temperature of electron plasma whose data has been generated via particle in cell simulation. My professor said if I have histogram of electron density by kinetic energy, then I can get temperature of the electron plasma when I apply the log on density. He also mentioned slope of log applied histogra... | 0 |
This question Sum of Countable Increasing Absolutely Continuous Functions is Absolutely Continuous says if the functions are all AC, then the sum is also AC. Then if the answer is not true for my question, we only need to consider the case of continuous singular functions. However, I have no clue how to deal with them ... | 0 |
The wave function collapses anyways whether I wanted to know which slit the electron passed through or not, the only difference there is that in the former case the wave function collapse for any electron at either of the two positions directly behind the slits, i mean the electron still in superposition of all possibl... | 0 |
Recently i have been reading "A radical approach to real analysis" by David Bressoud and this thing got stuck in my mind Here you might lose convergence at the end point is written in last paragraph what is this meant for an infinite trigonometric series .It has also some relation with derivatives somehow. This was wri... | 0 |
Let's say I put a neutral conducting sheet in front of a charge. What will happen to the sheet? If I place a plate with some thickness in front of the charge, charges will develop on the face of the plate to maintain the electric field inside the plate zero. There is no such thing inside the sheet, so how will it react... | 0 |
I'm using the article documentclass to write a simple document, but when i compile the code the tableofcontents look like this: From section "Progetti" there is no space between the number and the name. The code of the section is the following: I already tried to take out the subsubsection thinking it maybe was the cau... | 0 |
In P Halmos measure theory book it written A Sigma ring S generated by C, the class of compact subsets of X where X is locally compact Hausdorff Space. Then S has open set and sets of S is called Borel Sets. I am very confused. How a sigma ring generated by the class of compact set has open set. P Halmos Measure theory... | 0 |
For a new paper I am writing to IEEE journals (double-column formats), many important paragraphs suffer from the default hyphenation in LaTeX. Especially, I don't like the hyphenations given in the Funding Statement at the end of the paper. If I don't want hyphenations in some words such as "under", "Programme", "Excel... | 0 |
I was given this problem in physics class. My teacher said that they reached the ground at the same time, but when I tested it out (video), I got drastically different results. I showed the professor and asked him why real life and theory did not match up, and he said to just accept it and would not explain what is goi... | 0 |
Pretty straight forward question. Which of the following sentences is/are "correct"? They are simping on Korean players They are simping in Korean players They are simping for Korean players What I want to express is that a group of people feeling extreme sympathy for Korean players in a online international game. I've... | 0 |
I am learning the theory of large deviations. In so many results in the theory and from the very beginning in each book about this subject one starts by introducing a family of probability measures satisfying some properties and defined on some (Polish) space. I do not understand why one needs in some important context... | 0 |
In the ideal quantum information version of metrology, a maximally entangled state is viewed as the best resource for quantum metrology. The optimal phase uncertainty of the NOON state reaches to the Heisenberg limit. Later we have seen that for same average particle number, an entangled coherent state (ECS) outperform... | 0 |
I can get a bit overwhelmed trying to find which frac or h symbol corresponds to the output of a complex expression. An easy way is to copy paste into lyx and edit there as you can edit the output directly by clicking on the right symbol but that can cause context switches and might lead to using the mouse which might ... | 0 |
Imagine that a person is walking with a constant velocity along the horizontal plane and turns the fan on the filing into a circular motion. Then, after sometime the fan will achieve a constant velocity, Then derive a relation to know the relative velocity of the fan with respect to that person! Say the radius of the f... | 0 |
I know partial derivatives should be used to solve this, but I'm wondering is there any to find the plane using the vector method of getting the Normal vector and a point on the plane. In this case, we already have a point, we just need to somehow find the Normal vector. Also, is there any connection between Normal vec... | 0 |
In the communication network given below, link failures are independent, and each link has a probability of failure p. (consider the physical situation). A can communicate with B as long as they are connected by at least one path which contains only in-service links. Given that exactly five links have failed, determine... | 0 |
Title says it all really. As is commonly known, the trace of the density matrix must be one and the trace over the density matrix times an operator is the expectation value of that operator. If you instead add up ALL the entries of the matrix (perhaps times some function related to the row/column indices) does this rep... | 0 |
I would like to know the structure of the sentence and also meaning. Is the vision subject? What in the sentence is what? The vision to do today what is needed for tomorrow. Can I understand.. like this? the vision we do today is what we need for tomorrow. The sentence was part of a speech as follow. Reject pessimism a... | 0 |
Correct me if i am wrong but all circuits must follow the law of conservation of energy. And the energy is supplied by the action of source to create a potential difference by moving charges against electric field In a battery the energy of chemical reactions that create potential difference is equal to the energy used... | 0 |
Since the only thing a computer can do is modify its machine state, and you can always change from one state into another state (there exists such a program) and so each program is invertible; and if all the programs are deterministic, then associativity also makes sense. Two programs are considered equivalent iff they... | 0 |
I found one passage that I really cannot understand the grammar structure. The below is the problematic sentence. The crates feature voids, allowing large volumes of water sufficient surface area to seep back into the ground. - Source I think this sentence should be; The crates feature voids with sufficient surface are... | 0 |
I was going through the energy/mass equation and it is said that both of the said quantities are interconvertible. That made me think that if we try putting actual values into the equation, the interconversion is actually very large; speed of light itself is a large constant, and the product of its square and mass of a... | 0 |
A high voltage wire can either have an large excess of electrons (net negative charge density), or a large defect of electrons (net positive charge density). The voltage difference between the wire and the human can be positive or negative. Are both cases equally dangerous? Is there a difference between electric shock ... | 0 |
Suppose I have an equipotential surface S. Thus the electric field at each point on said surface is direction normal to the surface. Will the magnitude of this electric field be constant for all points on this surface? (This reasoning comes from the feeling that if the electric field strength were to differ, a closed l... | 0 |
Was is generally accepted as singular - 'a dog was in the garden', were, plural - 'some dogs were in the garden. So why is 'You was in the garden' so wrong, (you were in the garden) but have to be 'you were in the garden, singular and plural? It seems to be restricted to only the noun 'you', which could be singular or ... | 0 |
In Quantum Mechanics conservation laws are fundamental, I was thinking about spin altering models of interaction such as the Ising Model and realized that it isn't at all clear how angular momentum conservation occurs in such a situation. If there is spin flipping occurring where does the contrary compensating angular ... | 0 |
During JJ thomson experiment and similiar other experiments,they found that cathode rays were deflecting from its direction under magnetic fields and electric field,also the gold leaf attached to co-axial cylinders led to conclusion that the cathode rays are negatively charged,but later,By Putting a paddle wheel or fan... | 0 |
Are there any experiments done to verify the absence of forces caused by complex structural organisations in systems? Afaik, experiments in QM and Standard model QFT talk about the validity of the interactions in individual particles that are not in any complex sturctures. Experiments in Condensed matter physics involv... | 0 |
When the size of the observable universe was small as a proton what was the physical content of it? Was there a limit of particles in such a tiny volume with enormous high density and energy? Can we find more than one proton inside such a volume, can we assume that because an electron, a quark, or a photon are point pa... | 0 |
For example does a virtual electron have the same characteristic intrinsic values like mass, charge, magnetic moment etc. as a normal stable electron? Or can these range wildly and not having specific values for the case of the virtual particles and if yes don't you think that the term for example "virtual electron" is... | 0 |
While calculating electric flux through an uncharged ring kept near a charge, we tend to draw a spherical Gaussian surface that covers the ring by edges but while using the gauss law, we tend to take the entire circular region of ring as area bounded by it(just like we do for circular disk). However, the ring has elect... | 0 |
I decided to use the Maple software to help me solve dynamic optimization problems, and I found this final solution for T. (example in the picture). example What does the LambertW mean for the solution T? Can I get rid of this expression to express T in simple terms? Does theLambertW (including the expression inside it... | 0 |
i just started my study in organic semiconductor. I realized to increase conductivity, polarons are formed in the polymer backbone. From what i read due to localised energy state level by polaron that can exist in the band gap, the band gap is narrowed. My question is if why is can polaron exist in band gap while elect... | 0 |
The soundness of FOL is proved in meta-language(natural language) by proving every deduce rule is correct, so we feel peaceful using those rules to deduce. But the process of proving every deduce rule is correct also uses deduce rules in natural language. For example, proving the correctness of PC(Proof by Case) also u... | 0 |
At one time or another, you've probably inquired about something (perhaps online) and been met with the curt or critical response. It's meant to showcase their cleverness. It's more of a concealed boast than it is a help. Is there a word or phrase which calls out is the disingenuousness of the help, since it's not that... | 0 |
recently I was solving questions on uncertainty principle but never came across questions involving system of particles like combination of electron and alpha particle. I wanted to understand how to deal system of particles while solving uncertainty principle questions. My initial thought was to calculate total uncerta... | 0 |
Hi there my question is pretty much in the title. I have to create tables which are longer than one page. The caption needs to be above the table, it would also be a great extra option if i could rotate the text inside the cell and i would need an automatically adjustable cell width just like tabularX does. Do you have... | 0 |
I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory, but performing the same experiment many times would generate a distribution probability for the possible values of the observable, which is better than only expectation values. So why do we claim ... | 0 |
How the word livid came (according to Merriam-Webster) to have three different meanings (in addition to the default, 'furious', one)? As I see, it could mean blue-and-black pallid reddish. I mean, I know that all meanings are accepted, but is that so? If I say to someone My car is livid. won't they have any predisposit... | 0 |
I know that the search for Higgs would be quite pointless if there was no estimation of its mass. Namely the perturbative violation of unitatity, gave us an upper bound on its mass.Unitarity Constraints on Heavy Higgs Bosons I wonder if there are enough parameters in the Standard Model of particle physics, such that it... | 0 |
He brought some food to eat on the road. He found some beer to drink in the fridge. Is it only reality and sanity that keep us from taking the beer example to mean he would be squashed in the fridge like a contortionist, sipping a beer? Or do the verbs license, or if that is too strong, erect interpretive guide-rails f... | 0 |
People say my idols are Messi and Ronaldo(no hate) but I dont know why I am attracted to Physics and Math.It always amazes me, this is just a dumb question which i suppose is gonna be closed by midnight today but can someone teach me physics? I would love to and also do questions he/she gives me, it will be like a free... | 0 |
Latex IEEE format color problem As you can see the text after the figure until the end of the paper became light blue. But, it supposed to be black. I don't know what happened! I utilized both 'color' and 'xcolor' package in my paper. When I remove the highlighted text inside the paper, the problem is solved. But, I th... | 0 |
In accelerated pure rolling ,as we know velocity of the bottom most point is zero with respect to ground but what makes it to have zero tangential acceleration. If tangential acceleration is to be zero at that point ,it must have net force zero in horizontal direction.The ground applies friction on bottom most point, w... | 0 |
I want to write the i and j as one "ij", as can be seen in the Dutch language, in my LaTeX document, but can't figure out how to do it, even with ChatGPT! If someone knows more, please hit me up! It could be the case that this is just not possible as it is not that frequently used, especially not when actually typing i... | 0 |
I'm using xindy to create indeces. However, the default sort order is not sensible for uppercase and lowercase. Is there a way to create a .xdy file so that the uppercases are sorted in front of lowercases. Here is an example: A Abel....... Alex....... aboutism... account.... axis....... B Bible...... basics..... bigge... | 0 |
I read this thread of articles by Casher(quite marginal in terms of citation) where they show in certain realistic models SUSY is broken by non-perturbative effects. Explicit breaking of supersymmetry by non-perturbative effects The SUSY currents turn out anomalous. Now I want to add a twist: Does the anomaly survive e... | 0 |
Construct a triangle ABC when angle A, length of angle bisector from A and circumradius are given. Since angle A and circumradius are given, we can find out the length of BC. I can elaborate on the same further if you're interested... This seems like a simple problem but I can't get it. Thank you! In a circle with a ra... | 0 |
Hopefully my question is not out of order in this site. I am trying to weigh an object that is too wide/long for my weight scale. If just put it on top of it it tips over. So my solution is to place my hand on the 'short side' to prevent it from tipping over. Assuming I am not pushing (just holding my hand as an 'stopp... | 0 |
The statement of class existence theorem includes "F be a formula that quantifies only over sets" then there exists a class A such that it contains only sets and a set x is in A iff F(x) is true. I am curious to see an example which breakz this requirement and have a quantifier over classes, and what kind of paradox it... | 0 |
If the circulation is negative and flux is clearly not zero then will the flux also be negative? If a curve C and its vector field are going in opposite directions (meaning C is going clockwise and the vector field is going counterclockwise), then circulation will be negative. If the vector field is pointing outwards f... | 0 |
If I penetrate water's surface with needle (using hand) then Cohesive forces> Adhesive forces and water molecules climb up the needle (exactly like capillary action) and needle behaves hydrophilically and when I make it rest like mosquito's legs on water, it floats (mosquitos actually float on water due to surface tens... | 0 |
In PWT, the wave function depends on the positions of all the particles. Therefore the velocity of a given particle depends of the positions of the other, it's why the theory is non local. In the model why there is a single wave for all the particle and not a wave for each particle? So that the velocity of a given part... | 0 |
I want to know like for continuity of a function at a given point we can check the limit of the function at that point and the value of the function at that point but how to verify if a function is uniformly continuous or not over a given interval and all kind of interval that is for open , closed and semi open or clos... | 0 |
This figure is taken from Wolfram MathWorld. The site classified the third region as not simply connected, and I get it, but it isn't also multiply connected, since multiply connected means that I can connect any two points in the region with a curve that lies entirely in the region. However, it is clear that I cant co... | 0 |
the decision partition problem is Np-complete.Now I would like to proof that if a polynomial Algorithm exists for the decision Problem than another polynomial algorithm would exist too, that would give two sets A and B that fulfill the decision Problem.Clearly this problem is Np hard .I would like a hint or something t... | 0 |
Air can hold water in proportion to partial pressure of water vapor. This is affected by temperature. But is the water capacity of air also affected by ambient pressure? I did find some answers that water holding capacity of air decreases with increasing pressure. Quora link, UCAR link But I was unable to find any equa... | 0 |
I have a man-in-the-street question that was probably "predetermined". If everything around us is co-interacting particles whose source is some infinite small point that started their expansion into nothing due to the Big Bang, how come those particles have any interactions? They should become further with every second... | 0 |
Wikipedia asserts that The rays represent luminous intensity, which varies according to Lambert's cosine law for an ideal diffuse reflector. Describing this figure: I understand this is a perceptual phenomenon, and we are observing the light coming from an object that is diffusely - and isotropically - reflecting light... | 0 |
I understand that our main supporting evidence for dark matter is the anomalous speed of objects orbiting around the edges of distant galaxies. Is there a reason why dark matter solves this problem better than say, the strength of gravity simply being stronger in the region? My idea is that maybe these galaxies don't s... | 0 |
With Compton scattering the total momentum and the total energy of the photon electron system is conserved, so it has to be ELASTIC Collision/Scattering. But an argument is that just because the kinetic energy of the incoming photon is different than the outgoing photon, it is INELASTIC Collision/Scattering. However, I... | 0 |
If one plate of an isolated charged parallel plate capacitor is earthed, then that plate must have a potential zero after being earthed as that is what earthing an isolated conductor does, but potential on each plate is only due to the charges on the other plate. Since the other plate(the one which is not earthed) is i... | 0 |
In the dimensional analysis, relationship of dimensionless parameter is? Above is the previous question I asked. I kinda understand that relationship of dimensionless group can be more complex. However, I was taught using the above method to determine dimensionless groups. Then how should I interpret the last equation?... | 0 |
So I've heard that all finite abelian groups are isomorphic to direct sums of the integers or of integers modulo a power of a prime, then you get that all extensions of reals are basically the real numbers or the p-adic number. Is there any such theorem for the rationals? Any other way of creating numbers that is not s... | 0 |
Zenithal perspective projections are generated from a point P and carried through the sphere to the plane of projection as illustrated in the figure below. By a simple geometric relationship, we can show that the radius satisfies the following: with . The inverse equation is given by: where I could reproduce the first ... | 0 |
Okay so by the definition of a wave i.e The osciallatory disturbance in a medium which propogates energy is called as wave..the stationary wave contradicts both the crieteria as it doesnt propogate nor does it transmit any energy. Now one may say that a stationary wave is made by two progressive waves with same phase, ... | 0 |
In my physics high school lecture my teacher taught the concept of electromagnetic induction under diamagnetic materials (though not completely disregarded it in ferromagnetic substance but as a characteristic property of diamagnetic substance) but the typical high school numericals that are in my textbook consist of c... | 0 |
We know that volume is cubicly proportional to radius of a sphere. But if the radius is become half due to relativistic Length contraction, it's being reduced from only one dimension, not three. And the object is not a sphere any more . Does it mean that the volume in that case is directly proportional to radius? And i... | 0 |
Usually, when we study algebraic topology, we learn a lot of theory with just a few examples, like compact surfaces (orientable or not), wedge product of many circles, and a combination of those. Are these any slightly more complicated but special examples which shows important facts about the truth/falsity of some int... | 0 |
Arrow orbit around point C like graph show. Is motion of arrow, rotation or curvelinear translation according to physics definition? What is definition and types of translation and rotation? I find this: "When the paths of motion for any two points on the body are parallel lines, the motion is called rectilinear transl... | 0 |
Can anyone suggest a reasonably generalisable way to generate these marginal drop caps? The key features are that the drop cap may be more than one glyph long its width is scaled to fill the margin (minus a bit of white space for legibility) its height is scaled to a user-specified whole number of lines (nb. the first ... | 0 |
Our pre calculus teacher told us to start our mathematical investigation and he gave us three topics to explore to formulate a problem, a title and a our own formula that is novel or cannot be found in the google. Our group decided to focus on the third topic that was given which is algebra. So I would like to ask for ... | 0 |
I made a guess two years ago. I have a strong feeling that there is a proof using the fixed point theorem with geometric visualization, but I couldn't do the proof. If you have a simple closed convex curve, thr line Perpendicular to the tangent on the curve at both ends must be present If this feature is already known,... | 0 |
Bases for vector spaces are non-unique. Also, new bases can be generated from other bases very easily and formulaically. Is there some "prototype" basis, which we could find for every vector space, that defines a specific relationship between the elements in and across the different vectors for every possible basis for... | 0 |
My sense is that it never means an actual physical defect as in, "The quarterback's knees were shot -- he could still throw, but he knew that to management he was damaged goods." Or can it be used in the case of concrete damage to a person's body as the above example? It seems like for a simple medical issue, the term ... | 0 |
I cannot simply know where to use "port" and "interface", because these two words translate into one same word in my native language. So, I wanna figure out the difference between "port" and "interface", and when and where to use which. In my understanding (please correct me if I were wrong), the physical things, such ... | 0 |
I'm Finding it hard to visualize how higher pressure makes the boiling point higher. I understand how pressure increases then temperature increases such that say air molecules compressed gives it energy and then the molecules move fast and average kinetic energy increases hence temperature increases. But When we can sa... | 0 |
Let assume a metal tube open on one side having alpha emitter material on the other blocked side. Since alpha particles are blocked by the metal they will be emitted only through the open side and make thrust by the momentum of the alpha particles. Very small one, but continually accelerate the satellite. Partially dep... | 0 |
It seems like 'my sister and her' are both subjects so it should be 'my sister and she'... And it would be if they worked on something specific together (the obvious object). Eg: My sister and she work on this project. But the "together" at the end changes everything right? Unbundling the sentence it is clear that it i... | 0 |
I am given: Five points on the ellipse, The sharing center of the ellipse and the circle, And the circle. One of those five points is one of the intersections of a circle and an ellipse. Can we construct the three intersections of an ellipse and a circle that is not given? Blue ones are given, and greens are the points... | 0 |
For a conductor in an external field, I would like to know whether the electron clouds of each atom, just shift slightly (resulting in positive charges just on one edge, and negative charges just on the other with all internal area remaining neutral). Or, whether the electrons fully dissociate, leaving positive ions th... | 0 |
Question: When we only listen to the sound of that machine (TV), not watching its screen, which is appropriate to say "listen to the TV" or "listen to TV"? Background: When we watch that machine, we say "watch TV"; and when we put it work, we say "turn on the TV." I think these usage indicate that we use "the" when the... | 0 |
I had the following problem with the index: The alphabet order of the words in English: I have the order of capital letters come first then the order of small letters come next. I need the order to come according to the letters regardless of being capital or small. For example: Abed Dep Ced amid bned I need those words... | 0 |
I only recently thought about this, and I can't come to any conclusion. An explanation for ferromagnets is perhaps explainable, and my teacher said Quantum Mechanics complicates things since the magnetic behavior is distorted, given for ferromagnets their origin is the spin of the electrons. But what about materials th... | 0 |
In my notes the axiom of extensionality is that 'two equal sets contain the same elements', this language suggests to me that there are two different sets that happen to be equal, which suggests there is an infinite number of sets with the same elements. I see this definition given many places and it causes me some con... | 0 |
From school we know examples of energy conversions: from electromagnetic to electric, from electric to heat, from heat to electromagnetic, etc. However, obviously this almost has nothing to do with conversion, because as heat, as electricity, as friction, and so on are electromagnetic field energy. But what if there is... | 0 |
I recently learned that we always break components of force along and perp to direction of net acceleration (for simplification) So in problems involving circular motion.... We resolve forces along centripetal acc So in problems involving vertical circular motion...we break mg along centrifugal force(ofc working from n... | 0 |
Huygens principle. can we accordingly define refraction to be diffraction from an infinitesimal length slit? According to Huygens principle, sticking to classical physics terms. as long as slit length is at most a wavelength, spherical form of waves is maintained. If we look at propagation inside a homogeneous medium t... | 0 |
In PowerPoint, there are often nice three key point diagrams like (source: https://www.slideteam.net/performance-mapping-ppt-powerpoint-presentation-portfolio-graphics-pictures-cpb.html) or (source: https://www.slidegeeks.com/business/product/three-levels-relationship-marketing-examples-ppt-powerpoint-presentation-idea... | 0 |
From the following image, why do we still call it isotropic? if the density at A and B differ, I don't think it's enough to call it isotropic. In my opinion, material is only isotropic if when we choose some point, around it in all directions, properties are the same throughout the end of the material from that point, ... | 0 |
I know about the conditional sentences that go as following: "If I were he, I would have forgotten the whole lesson." In the sentence above, "he" is preferable to "him," but can it also be preferred in the following case? Whom can I trust, if not ___. a) he b) him I pardon, if this is related to conditional sentences. ... | 0 |
the xelatex compile output will automatic write some output in content folder, when compile in the root of project, there contains a content folder and it works fine. Now I tweak my command and add the -output-directory parameter like this: xelatex -output-directory=/Users/xiaoqiangjiang/Downloads/cquthesis/out/ main.t... | 0 |
Is this grammatically defective? The rides were fast and long, as well as exciting, despite my apathy. Context: I often find myself writing sentences that I don't want to reorder but may contain an error, and am ignorant of grammar, if not absolutely naive; I have confused chat-gpt, asking it this. Background: I unders... | 0 |
I am a student in robotic assocciation and I designed working spectrometer for UV-Vis emission spectrum. The issue is evoking emission spectrum. The spectrometer is designed to be working on board of martian rover. Can I evoke the emission by shining the rock samples with UV lamp or X-ray lamp? We can't use laser beams... | 0 |
I had a sentence like this in my manuscript: [describing some limitation] .... Some studies worked it around by combining the results of two models ... in the sense that those studies made a workaround for the limitation. The native speaker changed the bold term to "worked around it", but I am almost sure I know the or... | 0 |
Suppose a straight current carring wire of finite length if kept in a external magnetic field (perpendicular to its length say dot). I know initially it would experience a magnetic force of magnitude ILB due to drift velocity of charges inside wire but now the wire would gain velocity , but if I use lorentz law to find... | 0 |
It is often recommended to the particular symbol from MnSymbol that you require instead of importing the package entirely such as the answer by @egreg. What is the general process of doing this? What if I need several symbols? Is there a difference, say, if I need an arrow vs. delimiters? Not really a question, just a ... | 0 |
Wikipedia claims for the proof of Arrow's Impossibility Theorem that when Every voter in segment one ranks B above C and C above A. Pivotal voter ranks B above A and A above C. Every voter in segment two ranks A above B and B above C. (B and C may switch for segments one and two but not pivot) by IIA the societal outco... | 0 |
In the light clocks, time ticks via the motion of light and since speed of light is constant therefore when the clock is in motion ,the photon has to cover a greater distance by the perspective of an object at rest . So in the perspective of object in rest time ticks at slow rate but in other clocks such as mechanical ... | 0 |
So this was a test question, I answered that both cars have the same acceleration. Since the graphs for A and B both are straight lines, therefore, the acceleration of both must be zero. But the answer given to us was that both are moving with same velocity. These graphs are not always to scale, so I thought that the d... | 0 |
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