How do I understand Kinetic energy formula? $$\frac{mv^2}{2}= Kinetic Energy$$ Can you explain me? What is purpose of $v^2$, $mv^2$, I am trying to understand the formula.
Why does kinetic energy increase quadratically, not linearly, with speed? As  says:     [...] the kinetic energy of a non-rotating object of mass $m$ traveling at a speed $v$ is $\frac{1}{2}mv^2$.   Why does this not increase linearly with speed? Why does it take so much more energy to go from $1\ \mathrm{m/s}$ to $2\ \mathrm{m/s}$ than it does to go from $0\ \mathrm{m/s}$ to $1\ \mathrm{m/s}$?  My intuition is wrong here, please help it out!
What is the coefficient of the term $a^i b^j c^k$ in the expansion of $(a+b+c)^n$? What is the coefficient of the term $a^i b^j c^k$  in the expansion of   $(a+b+c)^n$ ?   Given solution:     Before collecting like terms, each term in the expansion is a product   of $n$ factors each  of which is $a, b,$ or $c$.  Those terms which   have exactly i a’s, j b’s and k c’s can be combined into   the single term $a^i b^j c^k$ and the number of such terms will be   equal to the number of n letter strings containing i a’s, j b’s and k   c’s, which by the Mississippi rule is $\frac{n!}{(i!\times j! \times  k!)}$.   I understand that this problem is actually about the derivation of the coefficient of the multinomial theorem,but I am not sure about the combinatoric reasoning,what I mean is that I understand the analogy problem but what I couldn't is how the analogy holds here,Could anybody explain this to me? Unable to get force:inputField or force:outputField to render inside other markup in Lightning Component when used in Lightning Experience Getting hybrid graphics to work nvidia-prime GT650M I recently made the switch to Ubuntu. Everything on my laptop works fine except my hybrid graphics card. It is Intel graphics combined with Nvidia GeForce GT650M. I tried Bumblebee, but primusrun doesn't work (segmentation fault, core dumped) and optirun works with glxspheres64, but steam games look worse with optirun than with Intel graphics (e.g. Surgeon Simulator 2013 runs fine with Intel and hangs a lot with optirun)   I tried Nvidia Prime, but it gives me a black screen on startup after install, so I can't do anything and have to power off my PC with the power button. I also tried nvidia-prime 0.5 on Ubuntu 14.04, and then I get 'low-graphics mode' and I can't get to Unity. Difference between $\mathbb C$ and $\mathbb R^2$ What are the basic differences between $\mathbb C$ and $\mathbb R^2$?  The points in these two sets are written as ordered pairs, I mean the structure looks similar to me. So what is the reason to denote these two sets differently? Legitimate edits of less than 6 characters I recently came across an  by  which contained a link to a specification that has since been moved. When attempting to edit the link, a change which involved the subtraction of only 4 characters, I ran up against the 6 character minimum requirement.  Ordinarily this would not be an issue. A less experienced poster would likely have other things within the answer that could be changed (). In fact, this seems to be the answer on every meta post relating to this topic (, , etc...).  The problem here, since I don't have 2k reputation, is that BalusC writes excellent answers... with the reputation to back them up. I don't feel there is anything in the post (besides the link) that would benefit from me editing.  What is the standard practice here?   Flag the post and explain my situation in the notes (for someone with higher reputation)? Comment on the post and hope that a) visitors read the comments or b) the OP gets notified and updates their post? Make edits, for the sole purpose of increasing characters, providing no benefit and possibly hurting the quality of the post?   For reference, the EL Specification in the post should be changed to , if someone wants to go ahead and take care of this. To estimate the time for brute-force attack we need to compute keyspace size divided by hash rate, where the hash rate (hash/second) varies depending on the computer's capabilities.  The website  shows the hash rate for different computers.  Can you explain the following two confusing phenomena?   The hash rate decreases as the message size increases. Core i3 has a higher hash rate than Core i7 for SHAKE128. What do I need for extreme macro photography? How to code an automated bot that can browse and do operations on a webpage setSystemUiVisibility(SYSTEM_UI_FLAG_LAYOUT_HIDE_NAVIGATION) does not work Create a variable in .CSS file for use within that .CSS file Possible Duplicate:          We have some "theme colors" that are reused in our CSS sheet.  Is there a way to set a variable and then reuse it?  E.g.  .css OurColor: Blue  H1 {   color:OurColor; } I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force holding a subatomic particle together? What keeps mass in it's state? I hope this is not a silly question but I am clueless. Thanks I have very old Computer  What's the Best Operating System for Old Computer? Resetting crontab file to default Pending suggested edit message bug I just tried to edit a post on Stack Overflow but when I pressed the 'edit' button it showed me this message on a white page.    I know what the message means but I don't think it is supposed to show up in a white page. So, is this a bug or is it something else? Chrome browser will not connect to intranet web addresses Why do my shortcut icons get broken on Windows 7? I have a strange problem. My icons seem to disappear randomly on my Windows 7. They were there a while back, now they ain't.  It happens often and quite randomly. Anyone know a fix? change thickness median line geom_boxplot() Extension of degree 2 with characteristic not 2 I am told that $K \leq L$ is a field extension of degree 2 and that $K$ has characteristic not 2. I am then asked to show that $\exists \: \alpha \in L$ such that $L = K(\alpha), \; \alpha^2\in K $  So far I have that:  $\exists \; \alpha_1, \alpha_2 \in L$ such that $L = K( \alpha_1, \alpha_2)$  $\Rightarrow |L:K| = |L:K(\alpha_1)| |K(\alpha):K| $ so $|K(\alpha):K| = 1$ or $2$  $|K(\alpha_1):K| = 2 \Rightarrow L = K(\alpha_1)$ and $deg(f_{\alpha_1}(t)) = 2  $ where $f_{\alpha_1}(t)$ is the minimal polynomial of $\alpha_1$ over $K$   So $f_{\alpha_1}(t) = t^2 + at + b$ for some $a,b \in K$  Also, $|K(\alpha_1):K|=1 \Rightarrow K(\alpha_1) = K$ and $L = K(\alpha_2)$ which means $degf_{\alpha_2}(t) = 2$ where $f_{\alpha_2}(t)$ is the minimal polynomial of $\alpha_2$ over $K$.   So $f_{\alpha_2}(t) = t^2 + at + b$ for some $a,b \in K$  Given that we consider the same polynomial each time, relabel to consider:   $f_{\alpha}(t) = t^2 + at+ b $ for some $a,b \in K$  We have already demonstrated that $L=K(\alpha)$ for some $\alpha \in L$ so now we much show that $\alpha^2 \in K$  $\alpha^2 \in K \Leftrightarrow a = 0_K$  I now have no idea how to show that this coefficient of $f_{\alpha}(t)$ is necessarily $0$.   I know that $f_{\alpha}(t)$ has two roots in $L$ and that because $K$ and thus $L$ has characteristic not 2, they cannot be the same root, but I don't know how to then conclude that they must sum to $0$  Any help would be greatly appreciated. Assuming i have a line that i want to add to a file without opening an editor.  How could i append this line  alias list='ls -cl --group-directories-first'   to this file  config.fish The  says that there is a moderator election occurring.   How does the election work and how can I get involved?