# Tagged Questions

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41k views

### How to get distance when acceleration is not constant?

I have a background in calculus but don't really know anything about physics. Forgive me if this is a really basic question. The equation for distance of an accelerating object with constant ...
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### Rigorous underpinnings of infinitesimals in physics

Just as background, I should say I am a mathematics grad student who is trying to learn some physics. I've been reading "The Theoretical Minimum" by Susskind and Hrabovsky and on page 134, they ...
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### How to treat differentials and infinitesimals?

In my Calculus class, my math teacher said that differentials such as $dx$ are not numbers, and should not be treated as such. In my physics class, it seems like we treat differentials exactly like ...
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### Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?

I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
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### Infinite series of derivatives of position when starting from rest

Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
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### Is Newton's first law something real or a mathematical formalism?

Why do objects always 'tend' to move in straight lines? How come, everytime I see a curved path that an object takes, I can always say that the object tends to move in a straight line over 'small' ...
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### What are the differences between the differential and integral forms of (e.g. Maxwell's) equations?

I would like to understand what has to be differential and integral form of the same function, for example the famous equations of James Clerk Maxwell: How to know where to apply each way? Excuse ...
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### Landau's derivation of a free particle's kinetic energy- expansion of a function?

I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact ...
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### What is divergence?

What is divergence? I was learning about Maxwells equations and don't understand the divergence part of it. Can someone give an intuition of what divergence is in relation to maxwells equation. To ...
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### Level of calculus required for physics [closed]

First time for me here so kindly let me know if I violate the rules - especially if this is a duplicate. After reading the page how to become a good theoretical phycist, I started a serious revision ...
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### Electromagnetic field and continuous and differentiable vector fields

We have notions of derivative for a continuous and differentiable vector fields. The operations like curl,divergence etc. have well defined precise notions for these fields. We know electrostatic and ...
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### Can someone give an intuitive way of understanding why Gauss's law holds?

Gauss' Law of electrostatics is an amazing law. It is extremely useful (as far as problems framed for it are concerned :D. I do not have a real world-problem solving experience of using Gauss' Law). ...
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### Wrong calculation of work done on a spring, how is it wrong?

So I would have thought that this would be how you derive the work on a spring: basically the same way you do with gravity and other contexts, use $$W=\vec{F}\cdot \vec{x}.$$ If you displace a spring ...
In Landau-Lifschitz, following expansion is given, We have, $$L(v'^2)~=~L(v^2+2\textbf{v}\cdot\epsilon+\epsilon ^2)$$ expanding this in powers of $\epsilon$ and neglecting powers of higher order, $$L(... 3answers 4k views ### What is the meaning of the third derivative printed on this T-shirt? Don't be a \frac{d^3x}{dt^3} What does it all mean? 2answers 599 views ### A basic math identity often used in integrals [closed] I'm just wondering about why y_i=A_{ij}x_j implies$$d^Ny=|\det A|d^Nx.$$I see that \det A is the product of the eigenvalues of a diagonal matrix but still don't exactly see how. Please help. 3answers 500 views ### Problem in deducing the equations of motion using indefinite integral As we know, antiderivative or indefinite integral is the function the derivative of which gives the actual function. Let F(x) be the derivative of f(x) ie. the instantaneous rate of change of f(... 1answer 1k views ### Newton's original proof of gravitation for non-point-mass objects Suppose we have two bodies, one very large (Earth), and one very small (a cannon ball). If the cannon ball is some distance away from the Earth, to find out the force produced on the cannot ball, we ... 3answers 218 views ### Is \dfrac{dx}{dt} a fraction or not? I am new to calculus and during my mathematics class my sir defined \dfrac{dx}{dt} as$$dx/dt=\lim_{t\to t_1}\dfrac{f(t)-f(t_1)}{t-t_1}$$and my sir made a clear statement that \dfrac{dx}{dt} ... 1answer 196 views ### Determine the flow and amplitude equation for thermal energy (with Del operator) It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a 3-Dimensional space ( e.g x\cdot y\cdot z = 4\cdot3\cdot2, a certain room/class of that size ... 2answers 843 views ### Gauss's (Divergence) theorem in Classical Electrodynamics How does divergence theorem holds good for electric field. How does this hold true-$$\iiint\limits_{\mathcal{V}} (\vec{\nabla}\cdot\vec{E})\ \mbox{d}V=\mathop{{\int\!\!\!\!\!\int}\mkern-21mu \...
In going from eq.(6.13) to (6.14) in http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf it is assumed that \displaystyle\int\dfrac{d\Omega_{\vec{p}}}{4\pi}\,(\hat{p}\cdot\hat{p})\...