\documentclass[10pt,a4paper]{article} % Packages \usepackage{fancyhdr} % For header and footer \usepackage{multicol} % Allows multicols in tables \usepackage{tabularx} % Intelligent column widths \usepackage{tabulary} % Used in header and footer \usepackage{hhline} % Border under tables \usepackage{graphicx} % For images \usepackage{xcolor} % For hex colours %\usepackage[utf8x]{inputenc} % For unicode character support \usepackage[T1]{fontenc} % Without this we get weird character replacements \usepackage{colortbl} % For coloured tables \usepackage{setspace} % For line height \usepackage{lastpage} % Needed for total page number \usepackage{seqsplit} % Splits long words. %\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely. \usepackage[normalem]{ulem} % For underlining links % Most of the following are not required for the majority % of cheat sheets but are needed for some symbol support. \usepackage{amsmath} % Symbols \usepackage{MnSymbol} % Symbols \usepackage{wasysym} % Symbols %\usepackage[english,german,french,spanish,italian]{babel} % Languages % Document Info \author{Mon. (Monz gomz)} \pdfinfo{ /Title (movimiento-rectilineo.pdf) /Creator (Cheatography) /Author (Mon. (Monz gomz)) /Subject (Movimiento rectilíneo Cheat Sheet) } % Lengths and widths \addtolength{\textwidth}{6cm} \addtolength{\textheight}{-1cm} \addtolength{\hoffset}{-3cm} \addtolength{\voffset}{-2cm} \setlength{\tabcolsep}{0.2cm} % Space between columns \setlength{\headsep}{-12pt} % Reduce space between header and content \setlength{\headheight}{85pt} % If less, LaTeX automatically increases it \renewcommand{\footrulewidth}{0pt} % Remove footer line \renewcommand{\headrulewidth}{0pt} % Remove header line \renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit % This two commands together give roughly % the right line height in the tables \renewcommand{\arraystretch}{1.3} \onehalfspacing % Commands \newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour \newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols \newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns \newcommand{\tn}{\tabularnewline} % Required as custom column type in use % Font and Colours \definecolor{HeadBackground}{HTML}{333333} \definecolor{FootBackground}{HTML}{666666} \definecolor{TextColor}{HTML}{333333} \definecolor{DarkBackground}{HTML}{839E29} \definecolor{LightBackground}{HTML}{F7F8F1} \renewcommand{\familydefault}{\sfdefault} \color{TextColor} % Header and Footer \pagestyle{fancy} \fancyhead{} % Set header to blank \fancyfoot{} % Set footer to blank \fancyhead[L]{ \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{C} \SetRowColor{DarkBackground} \vspace{-7pt} {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}} } \end{tabulary} \columnbreak \begin{tabulary}{11cm}{L} \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Movimiento rectilíneo Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{Mon. (Monz gomz)} via \textcolor{DarkBackground}{\uline{cheatography.com/64672/cs/23808/}}} \end{tabulary} \end{multicols}} \fancyfoot[L]{ \footnotesize \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{LL} \SetRowColor{FootBackground} \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\ \vspace{-2pt}Mon. (Monz gomz) \\ \uline{cheatography.com/monz-gomz} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Published 4th August, 2020.\\ Updated 4th August, 2020.\\ Page {\thepage} of \pageref{LastPage}. \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\ \SetRowColor{white} \vspace{-5pt} %\includegraphics[width=48px,height=48px]{dave.jpeg} Measure your website readability!\\ www.readability-score.com \end{tabulary} \end{multicols}} \begin{document} \raggedright \raggedcolumns % Set font size to small. Switch to any value % from this page to resize cheat sheet text: % www.emerson.emory.edu/services/latex/latex_169.html \footnotesize % Small font. \begin{multicols*}{3} \begin{tabularx}{5.377cm}{x{1.09494 cm} x{3.88206 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Cinemática}} \tn % Row 0 \SetRowColor{LightBackground} \seqsplit{Trayecto} & El camino que recorre un cuerpo. \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Rapidez & El número de metros recorridos en 1 segundo. \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \seqsplit{Mecánica} & Es el estudio del movimiento de los objetos \tn % Row Count 6 (+ 2) % Row 3 \SetRowColor{white} \seqsplit{Dinámica} & Es el estudio de las causas del movimiento \tn % Row Count 8 (+ 2) % Row 4 \SetRowColor{LightBackground} \seqsplit{Cinemática} & El estudio de la descripción del movimiento. \tn % Row Count 10 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Desplazamiento}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Construimos un {\emph{sistema de coordenadas}}, donde {\bf{x}} será la distancia y su dirección será la dirección del objeto (+ -).} \tn % Row Count 3 (+ 3) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{El desplazamiento es el cambio de posición de un objeto.} \tn % Row Count 5 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Tiene magnitud y dirección.} \tn % Row Count 6 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.53827 cm} x{2.43873 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de desplazamiento}} \tn % Row 0 \SetRowColor{LightBackground} Diferencia de posición. & \{\{ac\}\}{\bf{Δx = x2 - x1}} \tn % Row Count 2 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Rapidez y velocidad}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Describe qué tan rápido un objeto cambia de posición.% Row Count 2 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Pendiente}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{- Se define por la diferencia de posición de dos puntos y un intervalo de tiempo. \newline % Row Count 2 (+ 2) {\bf{- Indica la velocidad.}}% Row Count 3 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Es la inclinación de la gráfica.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.68758 cm} x{2.28942 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de la Pendiente}} \tn % Row 0 \SetRowColor{LightBackground} Intervalo de posición entre intervalo de tiempo & \{\{ac\}\}{\bf{m = (x2 -x1) / (t2 - t1)}} \tn % Row Count 3 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}--} \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\emph{La derivada de la posición respecto al tiempo es la pendiente en ese tiempo.}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Rapidez Media}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Describe que tan rápido se recorrió una distancia en un tiempo.% Row Count 2 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de Rapidez Media}} \tn % Row 0 \SetRowColor{LightBackground} Total de la distancia entre el total del tiempo. & {\bf{rapidez media = total distancia transcurrida / tiempo}} \tn % Row Count 3 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}--} \SetRowColor{LightBackground} \mymulticolumn{2}{x{5.377cm}}{{\emph{La rapidez es una cantidad escalar y siempre positiva.}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Velocidad promedio o media}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{{\bf{- Es el cambio de posición en el tiempo.}} \newline % Row Count 1 (+ 1) - Recibe el nombre ya que las medias (promedio) de desplazamiento total y del tiempo no indica nada sobre el movimiento entre los puntos. \newline % Row Count 4 (+ 3) - La trayectoria pudo ser curva o recta.% Row Count 5 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.78712 cm} x{2.18988 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de Velocidad Media}} \tn % Row 0 \SetRowColor{LightBackground} Qué tan rápido se cambia de posición. & \{\{ac\}\}{\bf{Vm = (x2-x1) / (t2-t1)}} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} Donde x2-x1 es desplazamiento & \{\{ac\}\}{\bf{Vm = Δx / Δt}} \tn % Row Count 4 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Velocidad Instantánea}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Es la velocidad en un instante de tiempo.% Row Count 1 (+ 1) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{Un tiempo específico o un intervalo muy corto.} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de Velocidad Instantánea}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1596552540_material-ucGxWKj4.png}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\emph{Limite de la Velocidad m con Δt = 0}} \newline {\emph{Es la derivada de la posición respecto a un tiempo.}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Aceleración}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Es el cambio de velocidad respecto a un tiempo dado.% Row Count 2 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Aceleración media o promedio.}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Igual que la Velocidad media, es la aceleración en un intervalo de tiempo% Row Count 2 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\emph{Se mide en m/s\textasciicircum{}2\textasciicircum{}}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{x{2.93643 cm} x{2.04057 cm} } \SetRowColor{DarkBackground} \mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de Aceleración Media}} \tn % Row 0 \SetRowColor{LightBackground} Cambio de velocidad en el tiempo & {\bf{am=(v2-v1)/(t2-t1)}} \tn % Row Count 2 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}--} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Aceleración instantánea}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{O solo aceleración, donde es en un intervalo muy corto de tiempo o un tiempo específico dado.% Row Count 2 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Fórmula de aceleración instantánea}} \tn \SetRowColor{LightBackground} \mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/monz-gomz_1596557299_aceleracion-instantanea-mrav.jpg}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{{\emph{Es la 2ª derivada del desplazamiento}}} \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Movimiento en Aceleración Constante}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{Donde la aceleración cambia constantemente en el tiempo.% Row Count 2 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Algunas fórmulas para la aceleración constante}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{V = at + V0}}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{Vm = (V0 + V)/2}}} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{x = (at\textasciicircum{}2\textasciicircum{}/2) + V0t + X0}}} \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{t = (V-V0)/a}}} \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{V\textasciicircum{}2\textasciicircum{}= V\textasciicircum{}2\textasciicircum{}0 + 2a(x-x0)}}} \tn % Row Count 5 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Caída Libre}} \tn \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{- Cuando un cuerpo cae libremente donde no hay fuerza ajena a su peso que altere el movimiento. \newline % Row Count 2 (+ 2) - La aceleración debido a la {\bf{gravedad}} es dado por {\bf{g que vale a 9.81 m/s\textasciicircum{}2\textasciicircum{}}}% Row Count 4 (+ 2) } \tn \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{5.377cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Fórmulas de caída libre}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{h = 1/2 gt\textasciicircum{}2\textasciicircum{}}}} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{V= -gt + V0}}} \tn % Row Count 2 (+ 1) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{y = (-gt\textasciicircum{}2\textasciicircum{}/2) + V0t + y0}}} \tn % Row Count 3 (+ 1) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{V\textasciicircum{}2\textasciicircum{}= V\textasciicircum{}2\textasciicircum{}0 -2g(y - y0)}}} \tn % Row Count 4 (+ 1) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\}{\bf{V=raizcuadrada(2gh)}}} \tn % Row Count 5 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}