Assume there are no other forces acting and the rocket+fuel described do not weigh anything. Also, by rocket I mean engine/thruster, not space shuttle.  Suppose you have a planet, say of mass 1,000,000,000 kg and you push it with a rocket which exerts a force of 1 N. This will accelerate the planet by $10^{-9}\, m/s^2$.  Then, suppose you have a feather of mass 0.005 kg and push it with the same rocket which exerts a force of 1 N, accelerating it by $200\, m/s^2$.  It follows that the feather will traverse a distance of 1 m much faster than the planet and thus spend much less rocket fuel to do so. So, the energy used to propel the planet must be much more than the energy used to propel the feather.  But, work done = force &times; distance, $1 \times 1 = 1\, J$ for both the planet and the feather. I think I have misunderstood something. How is this possible?
The change in energy of an object can be determined by the work equation, where work is the change in energy:  $$ W = F \cdot d $$  I conceptualize the transfer of energy as simply a series of small "packets" of energy being transferred at every Planck length. These small "packets" of energy add up to the total energy transferred (i.e. work). I'm not sure if this conceptualization is correct, so correct me if I am wrong.  However, it makes me wonder why the amount of energy transferred is dependent on distance and not time.  $$ m_1 = 10~kg \\ m_2 = 20~kg \\ W_1 = (10~N)\cdot(5~m) = 50~J \\ W_2 = (10~N)\cdot(5~m) = 50~J \\ W_1 = W_2 \\ t_1 \neq t_2 $$  If I apply a constant force on an object, why isn't the energy transferred at a constant rate with respect to time? The energy transfer rate varies dependent on how long it takes to cover the set distance.  In other words: why is the energy transferred consistent per unit of distance, and not per unit of time?
"Open in Terminal" in Ubuntu 18.04 This option seems to have gone away after upgrading from Ubuntu 16.04. I tried installing nautilus-open-terminal but it is unable to locate the package for 18.04. Also trying to install nautilus-actions gives:  Package nautilus-actions is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source     How to fix this? Is it really incorrect to start a sentence with "and"? I know it's wrong, but I do it all the time or else my sentences would go on forever. Restricting SSH sessions for accounts on ubuntu server May someone please show me how I would restrict accounts/people logging into an ubuntu 10.04 server by SSH to a single active session at a time for each account that logs into the server.  Regards Why do paintbrush loops get thicker at the top in Illustrator? When I do swirls in Illustrator with the paintbrush tool I often get this result (see image).    The loops doesn't get perfectly rounded, instead sometimes some of them gets thicker at the top of the loop... It tends to happen more if I paint small with low brush sizes. Why is this happening? I'm using a Samsung I9000 and I have some annoying apps that came pre installed by the phone vendor, like a music store, a custom web browser and other memory leaking apps.  Those crappy apps can't be uninstalled neither by Manage applications tool, nor by editing the apps tiles in the front menu.  I guess I have to be a root user or something to get rid of those apps, but I don't know how. Find $a$ such that $(x+a)(x+1991)+1=(x+b)(x+c)$ with $a,b,c\in\Bbb Z$ Find all integer values of $a$ such that the quadratic expression $(x+a)(x+1991)+1$ can be factored as a product $(x+b)(x+c)$ where b and c are integers.   I tried to do it by comparing the two expressions but I can't proceed. Limit of $(\cos1/n)^{n^2}$ when $n\to\infty$ I've been trying to solve this limit: $$\lim_{n\to \infty} \left(\cos\left(\frac{1}{n}\right)\right)^{n^2}$$ I solved it using l'hopital but I have to try in another way. I tried to make the expression:  $$ \lim_{n \to \infty}\exp\left(n^2\ln\left(\cos\left(\frac{1}{n}\right)\right)\right)$$  but it didn't work out for me... Lazy loading properties after an insert Kolmogorov-Smirnov two-sample $p$-values I am using the Kolmogorov&ndash;Smirnov two-sample test to compare distributions, and I noticed a $p$-value is frequently reported as the test statistic. How is this $p$-value determined? I know it's the probability of obtaining a result at least as large as the one obtained, but how is this $p$-value determined given this is a nonparametric test? That is, we can't assume Gaussian fluctuations in the distribution and compute the $p$-value using a $t$-test.  Thanks! How can I easily encrypt a file? Is there any simple (IE: right click in Nautilus) way to password protect a particular folder/file in Ubuntu? I've got a few files containing sensitive info and I'd much prefer that if/when I leave my computer alone, they aren't accidentally accessed by someone else.  The secruty does not have to be extremely tight. My only concern is that when family/friends come over, I don't really like the idea of them looking at my bank details, accounts or, you guessed it, porn collection.  A simple, effective way to let me put my machine in the hands of someone else knowing that said machine can not cause me embarresment is the sole reason why I'd like to see this in Ubuntu. Why double-headed arrows when the direction of node is specified? I am quite puzzled when drawing the connection of nodes.  \usepackage{xcolor} \definecolor{darkblue}{HTML}{1F4E79} \definecolor{salmon}{HTML}{FF9C6B} \tikzstyle{cell} = [rectangle, minimum width=1cm, minimum height=0.5cm,text centered, draw=black, fill=salmon] \tikzstyle{state} = [rectangle, minimum width=1cm, minimum height=0.5cm,text centered, draw=black, fill=darkblue] \tikzstyle{arrow} = [thick,-&gt;,&gt;=stealth]  \begin{tikzpicture}[thick,scale=0.8, every node/.style={scale=0.8},node distance=1.5cm]     \node (0) [state] {\textcolor{white}{feature extraction}};     \node (1) [cell, below of=0] {invertBotConE2\_f48\_k1\_b4\_noskip};     \node (2) [cell, below of=1] {invertBotConE2\_f16\_k3\_b4\_noskip};     \draw [arrow] (0) -- (1);     \draw [arrow] (1) -- (2);     \draw  (0.east)  [arrow]  edge [out=0, in=0, out looseness=4, in looseness=4]  (2.north); \end{tikzpicture}   0,2 are my nodes. When east is specified, it creates an arrow on node 0. If removed, it disappears. What if I would like to put 0.south as the start of the edge? I am able to solve simple differential equations like :  $$\dfrac{dy}{dx} = 3x^2 + 2x$$  We simply bring $dx$ to other site and integrate.  But how do we find solutions of differential equations like :  $$\frac{d^2x}{dt^2} + \dfrac{kx}{m} = 0$$  ?  We have been told the solution is $x(t) = A\cos ( \omega t + \phi_o)$ where $\omega\ =\sqrt{\dfrac{k}{m}}$  but how do we actually find it? Script Tag Error - Aura Lightning Component How to increase the Java stack size? How do I save a file with managed_file in a theme? I'm developing a theme that it requires to have a header image on the front page, so I have this.  casper.theme  function casper_form_system_theme_settings_alter(&amp;$form, &amp;$form_state) {  $form['theme_extra']['front_page_background_image'] = array(     '#type' =&gt; 'managed_file',     '#title' =&gt; 'Front Page Background Image',     '#description' =&gt; 'Add background image for the front page',     '#required' =&gt; FALSE,     '#weight' =&gt; -4,     '#upload_location' =&gt; file_default_scheme() . '://theme/backgrounds/',     '#default_value' =&gt; theme_get_setting('front_page_background_image' , 'casper'),     '#upload_validators' =&gt; array(         'file_validate_extensions' =&gt; array('gif png jpg jpeg'),     ),  ); }   However, after it, while the file been missing and after some reading, I find out that is because managed_file does not save your image permanent.   There are similar questions:    is specified to Drupal 7.  is using "file" type instead of managed_file. I already tried something similar to what the Mayo theme is doing, but I was not able to successfully figure it out.   How can I save my image permanently? How to install Windows 7 after Ubuntu and dual boot? I just installed Ubuntu, a full install removing the prior OS. I was forced to remove  from my  because of the max four partitions already being there. I didn't lose anything, all backed up. However, now I am looking to create another partition and install Windows&nbsp;7 on it.   Do I also need some sort of boot loader that lets me choose which to boot? In attempting to wrap my mind around the basic vocabulary, concepts, and methods of philosophy, I find myself wondering what the difference is between a philosopher and a theologian.   can have two meanings: 1. Theology is a rational study of the existence of God/gods and the nature of religious ideas. 2. Theology is simply a study of a particular religion (or all religions), really more the practice than the theory, but maybe a mixture.  It seems from an immediate reading that definition 1 would lead to the conclusion that a theologian is a philosopher (perhaps that theology is a branch or subset of philosophy), but definition 2 appears to be rather unphilosophical in nature.    So, how does philosophy answer this question?   Is theology considered a proper subset/branch of philosophy overall? Does it depend entirely on which of the above 2 definitions of theology fits a particular theologian as to whether he is a philosopher or not?   I think this answer is simple and fairly self-evident, but somewhere in my gut I feel like I'm missing something.  Is there a treatment of this question in the literature?    Edit: the answers so far seem to want to redefine theology or other terms - that is fine, but please be clear that you are redfining them, and provide, if possible, sources for why the term should be different than given (support from historical works, other sites, etc.). Proof of conservation of energy? How is it proved to be always true? It's a fundamental principle in Physics based on all of our currents observations of multiple systems in the universe. Is it always true to all systems? Because we haven't tested or observed them all. Would it be possible to discover/create a system that could lead to a different result? How are we 100% sure that energy is always conserved? Finally, why did we conclude it's always conserved? What if a system keeps doing work over and over and over with time? The  of March 01, 2013 put it's distance at 14 hrs 04 mins 23 secs of light-travel time from Earth. A  (earlier today) tweet says it is 14 hrs 04 mins 22 secs of light-travel time from Earth. An  tweet put it still further out at 14 hrs 04 mins 25 secs of light-travel time.  The Voyager 2 tweets on Voyager 1's proximity to Earth too has reduced similarly to  earlier today from  reported on Feb 28 2013  It could quite simply be a typo ... If not a typo then my curiosity is piqued; I was under the impression the Voyagers are outbound from the Solar System now without any major in-system activities now.   How is it the Voyagers are closer to Earth than before? I'm having some problems with listings and UTF-8 in my document. Maybe someone can help me? Some characters work, like é and ó, but á and others appear at the beginning of words...  \documentclass[12pt,a4paper]{scrbook} \KOMAoptions{twoside=false,open=any,chapterprefix=on,parskip=full,fontsize=14pt}  \usepackage[portuguese]{babel} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{listingsutf8}  \usepackage{inconsolata} \lstset{     language=bash, %% Troque para PHP, C, Java, etc... bash é o padrão     basicstyle=\ttfamily\small,     numberstyle=\footnotesize,     numbers=left,     backgroundcolor=\color{gray!10},     frame=single,     tabsize=2,     rulecolor=\color{black!30},     title=\lstname,     escapeinside={\%*}{*)},     breaklines=true,     breakatwhitespace=true,     framextopmargin=2pt,     framexbottommargin=2pt,     extendedchars=false,     inputencoding=utf8 }  \begin{document} \begin{lstlisting} &lt;?php  echo 'Olá mundo!'; print 'Olá mundo!'; \end{lstlisting}  \end{document} \end{lstlisting}