The first equation of motion is $v = u + at$. The second equation of motion is $s = ut + \frac{at^2}{2}$. If we divide the second equation of motion by time $t$, why don't we get the first equation of motion where has $1/2$ come from?
I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$?
If I do not edit the .bashrc or other config files, the environment variables that I've setted are gone when I logout, or turn off the terminal.   What I'm curious is, where are those 'temporary' env vars saved in?   As I guess, they might be in the memory. That makes sense because they will disappear when the terminal is turned off(equals the terminal I was using is gone from the memory). Am I correct? Tracing a monochrome image into a 3D, extruded object with a script Who do you have to contact to obtain a license to stream manga? I am curious to know who the copyright holder to a manga is: is it the mangaka, or the publisher (such as Kodansha, Shonen Jump, etc)?  Who do you have to contact to obtain a license for streaming it? Quotient rings of Gaussian integers I used this isomorphism today but now I'm having trouble justifying it. The norm function isn't additive so I can't come up with a ring isomorphism to prove the following:     For any $\,a+bi\in\Bbb Z[i],\,\gcd(a,b)=1$, we have a ring isomorphism   $$\Bbb Z[i]/\langle a+bi\rangle\,\cong\Bbb Z/(a^2+b^2)\Bbb Z=:\Bbb Z_{a^2+b^2}.$$   Could someone show me an isomorphism between these rings to prove this? centering column headers in siunitx table column Could authors overturn recent community review decisions? When new users edit a post, the review is posted to a review queue and other reputable users can review the edit and choose to approve or reject it. However, I feel that a lot of people do it pretty quickly.    to . He was fixing broken links in the answer, and as soon as I saw it I knew it would have been a good edit. However, only one reviewer found so, and three others rejected it. I ended up manually doing the edit, and poor Onato didn't get any credit for it (in fact, he got an undeserved 'rejected' for it).  The point I want to bring is that, first and foremost, the person who wrote the answer probably knows best if an edit is acceptable or not. Could there be a time frame where the author of the answer (or question) can overturn a review decision?    EDIT: one more  was rejected by overeager reviewers as well. I absolutely disagree with the notion that the community knows better. The community repeatedly proves that it only wants Internet points.    EDIT: I told a commenter to fix something himself in one of my posts, but . I went back and applied the changes myself. It's not credited to him and his stats got a rejected edit now (which really should be an approved edit). The reason ("This edit is incorrect or an attempt to reply to or comment on the existing post") is blatantly wrong and shows once more that the community has much less insight into edit quality than the people who wrote the answers in the first place. It's true that the UI didn't make it easy for them, but those guys clearly didn't read the comment thread; I did, because as the author, I was notified.    EDIT: This time around, a user fixed a blatant (though small) mistake in one of my accepted answers. One hour later, another, unrelated 10k user , even though it had been approved by the community. I went back to undo his undo.  This goes on again to show that an active user is the best judge for the quality of an edit, and that since I can have the last word on edits on my own posts, I should be allowed to retroactively overturn a community edit vote and accordingly credit the person who proposed the change.    EDIT I wrote a  years ago. Some guy found it and tried to fix it but the community thought that it wasn't worth it. I think that the changes are great and once more I'll integrate them by myself into my post. Unfortunately for this user, he won't be credited for it. I still don't understand why I can't have a binding vote on edits on my posts. Math Induction Proof: $(1+\frac1n)^n < n$ So I have to prove:      For each natural number greater than or equal to 3,   $$(1+\frac1n)^n&lt;n$$   My work: Basis step: $n=3$ $$\left(1+\frac13\right)^3&lt;3$$ $$\left(\frac43\right)^3&lt;3$$ $$\left(\frac{64}{27}\right)&lt;3$$ which is true.  Now the inductive step, assume $P(k)=\left(1+\frac1k\right)^k&lt;k$ to be true and prove $P(k+1)=\left(1+\frac1{k+1}\right)^{k+1}&lt;k+1$.   This is where I am stuck because usually you add or multiply by $k+1$ or some similar term. Among other sources,  states that triple DES using three seperate keys (k1, k2, k3) is vulnerable to meet-in-the-middle-attacks, while triple DES using only two keys (k1, k2, k1) is not.  Why is this attack possible if all the keys are different, but not if the first and the third are the same? How to add a new kernel to grub2 How can we add a kernel to grub2? i knew the stuff we could do with the former versions, but it seems to have changed. What files should we edit? Escaping HTML strings with jQuery Does anyone know of an easy way to escape HTML from strings in ?  I need to be able to pass an arbitrary string and have it properly escaped for display in an HTML page (preventing JavaScript/HTML injection attacks).  I'm sure it's possible to extend jQuery to do this, but I don't know enough about the framework at the moment to accomplish this. Let $\{E_i\}_{i=1}^n$ be finitely many disjoint sets of real numbers (not necessarily Lebesgue measurable) and $E$ be the union of all these sets. Is it always true that  $$ m^\star (E)=\sum_{i=1}^N m^\star(E_n) $$ where $m^\star$ denotes the Lebesgue outer measure? If not, please give a counterexample. The Vitali set is a counterexample in the countable case, but I am not sure whether it is false in finite case. invalid EFI file path on windows 8 Unfair 3 Sided Die Question Say you have an unfair 3-sided die.  Side 1 will be rolled with probability $P_1.$ Side 2 will be rolled with probability $P_2.$ Side 3 will be rolled with probability $P_3.$  Find a formula for the probability that the 8th 3 will be rolled on the 10th roll.  Here is how I started:  $$ \sum_{i=8}^{10}P(T_8 = i) $$  Im just having trouble with that expansion? What happens to Bruce Banner when Hulk loses a tooth? In Age Of Ultron we witnessed Hulk lose a tooth.   My question is: Has Bruce Banner lost a tooth as well? 17.10 Super key to open applications Is the set of all functions $f:Z_+\rightarrow Z_+$ that are eventually constant countable. I just created a plane and added a wave modifier to it, to simply make it look like something fluid. Now, I have an Object that I want to place on the surface of this fluid plane. But how do I do that?  I thought of adding a driver to my Objects location, but I have no clue how to get the location of a certain vertex in runtime. Clearly, if Wolverine bleeds on the ground, a new Wolverine doesn't reconstitute himself from the drop. Presumably, if somehow his arm could be severed, that wouldn't happen there, either. If his head were cut off...probably not either.  So it seems that there's a minimum amount of contiguous body mass Wolverine has to have from which he can heal.  Maybe limbs are the limit...are there examples of Wolverine regenerating a lost limb? If so, well, this question. If not, is there anything else in the canon to suggest an answer? "None" as plural indefinite pronoun Deriving Newton's Third Law from homogeneity of Space