{"id":34449,"date":"2021-09-08T13:00:31","date_gmt":"2021-09-08T13:00:31","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34449"},"modified":"2025-09-08T03:26:52","modified_gmt":"2025-09-08T03:26:52","slug":"motus-rectilineus-uniformiter-acceleratus-mrua","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformiter-acceleratus-mrua\/","title":{"rendered":"Motus Rectilineus Uniformiter Acceleratus (MRUA)"},"content":{"rendered":"<p><center><\/p>\n<h1>Motus Rectilineus Uniformiter Acceleratus (MRUA)<\/h1>\n<p>    <em><strong>Summarium:<\/strong><br \/>\n    In hac lectione recognoscemus notionem motus rectilinei uniformiter accelerati (MRUA). Explicabitur quomodo hic motus accelerationem constantem in linea recta implicet et per aequationes ex integratione obtentas exprimatur.<\/em><\/p>\n<p>    <strong>Proposita Discendi:<\/strong><br \/>\n    Huius lectionis fine, discipulus poterit:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>Intelligere<\/strong> notionem motus rectilinei uniformiter accelerati (MRUA) eiusque proprietates.<\/li>\n<li><strong>Deducere<\/strong> aequationes itineris pro MRUA ex acceleratione constanti.<\/li>\n<li><strong>Applicare<\/strong> aequationes MRUA ad analysim et solutionem problematum motus unius dimensionis.<\/li>\n<li><strong>Interpretari<\/strong> condiciones initiales et constantes in aequationibus MRUA.<\/li>\n<\/ol>\n<p>    <strong>INDEX CONTENTORUM<\/strong><br \/>\n    <a href=\"#1\">Quid est motus rectilineus uniformiter acceleratus?<\/a><br \/>\n    <a href=\"#2\">MRUA et casus de Lapsu Libero<\/a><br \/>\n    <a href=\"#3\">Exercitia de motu rectilineo et uniformi<\/a><br \/>\n    <\/center><\/p>\n<p>    <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/P21bsNFF9Fw\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>Quid est motus rectilineus uniformiter acceleratus?<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=P21bsNFF9Fw&amp;t=143s\" target=\"_blank\" rel=\"noopener\"><strong>Motus rectilineus uniformiter<\/strong><\/a> acceleratus, MRUA breviter, est genus motus quod implicite iam tractavimus, quod apparebit cum inspiciemus modum quo ex aequationibus itineris exprimitur. Sed si descriptionem celerem volumus, MRUA est genus motus in quo acceleratio est constans, tam secundum magnitudinem quam directionem, et qui in linea recta evolvitur; id est, in una dimensione.<\/p>\n<h3>Motus rectilineus uniformiter acceleratus ex aequationibus itineris<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=P21bsNFF9Fw&amp;t=395s\" target=\"_blank\" rel=\"noopener\"><strong>Obtentio MRUA est<\/strong><\/a> imitatio directa laboris quem egimus ad obtinendas aequationes itineris per integrationem in prioribus lectionibus. Cum MRUA sit motus cum acceleratione constanti et unidimensionali, satis est deductiones facere super unicum axem coordinatum; si ratiocinamur super axem <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> consequimur hoc:<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\na_x(t) &amp; =&amp; a_{0x} \\\\ \\\\\n\nv_x(t) &amp; =&amp;  \\int a_{0x}dt = a_{0x}t + v_{0x} \\\\ \\\\\n\nx(t) &amp; =&amp; \\displaystyle \\int v_{x}(t)dt = \\frac{1}{2}a_{0x}t^2 + v_{0x}t + x_0\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: justify;\">Hic <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_{0x}, v_{0x}<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> sunt omnes constantes, et duae ultimae sunt constantes integrationis. Et hoc modo habemus exemplar completum motus rectilinei uniformiter accelerati secundum directionem axis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/span>. Ratiocinatio pro quolibet alio axe est omnino similis.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>MRUA et casus Lapsus Liberi<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=P21bsNFF9Fw&amp;t=512s\" target=\"_blank\" rel=\"noopener\"><strong>Unus e casibus maxime repraesentativis<\/strong><\/a> MRUA est lapsus liber. Hic est motus rectilineus uniformiter acceleratus qui verticaliter evolvitur et a gravitatis acceleratione producitur. Huius exemplar per aequationes itineris est sequens:<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\na_y(t) &amp; =&amp;  -g \\\\ \\\\\n\nv_y(t) &amp; =&amp;  -gt + v_{0y} \\\\ \\\\\n\ny(t) &amp; =&amp; \\displaystyle - \\frac{1}{2}gt^2 + v_{0y}t+ y_0\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: justify;\">Hic acceleratio gravitatis est <span class=\"katex-eq\" data-katex-display=\"false\">g=9,81[m\/s^2]<\/span>. Commune in lapsu libero est ut initio ex quiete incipiat (<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_{0y}=0<\/span><\/span>) et cum altitudine initiali <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y_0=h<\/span><\/span>, ita ut aequationes redigantur ad<\/p>\n<p style=\"text-align: justify;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\na_y(t) &amp; =&amp; -g \\\\ \\\\\n\nv_y(t) &amp; =&amp; -gt \\\\ \\\\\n\ny(t) &amp; =&amp; \\displaystyle - \\frac{1}{2}gt^2 + h\n\n\\end{array}\n\n<\/span>\n<p style=\"text-align: justify;\">Non refert quas aequationes habeas, hoc iam sufficit ut informationem ex his elicias \u00abrectas quaestiones ponendo\u00bb aequationibus.<\/p>\n<h4>Si corpus ex quiete incipit ex altitudine <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span><\/h4>\n<h5>Quantum temporis cadit?<\/h5>\n<p style=\"text-align: justify;\">Si hoc aequationibus quaerimus, illae nobis dicent \u00abcorpus terram tangere cum altitudo nulla est\u00bb, id est <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y(t)=0.<\/span><\/span> Si hoc fit, tum debemus tempus solvere in aequatione <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{1}{2}gt^2 + h = 0.<\/span><\/span> Ex hoc duo eventus possibiles habentur:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle t=\\pm\\sqrt{\\frac{2h}{g}}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Tempus negativum ad praeteritum spectat, et positivum ad futurum. Cum lapsus in futuro eveniat, possumus tempus lapsus definire ut<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle t_{lapsus}=+\\sqrt{\\frac{2h}{g}}<\/span><\/span><\/p>\n<h6>Qua celeritate terram attingit?<\/h6>\n<p style=\"text-align: justify;\">Hanc quaestionem respondere possumus simpliciter substituendo tempus lapsus in aequationem velocitatis. Si hoc facimus, consequimur velocitatem lapsus:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle v_{lapsus} = v_y(t_{lapsus})=-g\\sqrt{\\frac{2h}{g}}=-\\sqrt{\\frac{2g^2h}{g}} = -\\sqrt{2gh}<\/span><\/span><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Exercitia ad motum rectilineum et uniformem pertinentia<\/h2>\n<ol style=\"text-align: justify;\">\n<li>Mobile transit per originem cum velocitate initiali <span class=\"katex-eq\" data-katex-display=\"false\">v_0=10[km\/h]<\/span> et cum acceleratione <span class=\"katex-eq\" data-katex-display=\"false\">a_0=\\displaystyle \\frac{20[km\/h]}{5[s]}.<\/span>\n    Calcule positionem et velocitatem mobilis in momentis a) <span class=\"katex-eq\" data-katex-display=\"false\">t=5[s],<\/span> b) <span class=\"katex-eq\" data-katex-display=\"false\">t=10[s],<\/span> c) <span class=\"katex-eq\" data-katex-display=\"false\">t=15[s]<\/span> et d) <span class=\"katex-eq\" data-katex-display=\"false\">t=1[min].<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=P21bsNFF9Fw&amp;t=1329s\" target=\"_blank\" rel=\"noopener\"><strong>[SOLUTIO]<\/strong><\/a><\/li>\n<li>Homo relinquit globum ferreum et lapidem ex altitudine 20[m] simul ex quiete. Utraque corpora eandem magnitudinem habent, sed pondus diversum. Quantum temporis cadunt et qua velocitate moventur momento quo terram attingunt?; Potestne unum ex his corporibus citius cadere quam alterum aut maiore velocitate pervenire? <a href=\"https:\/\/www.youtube.com\/watch?v=P21bsNFF9Fw&amp;t=1873s\" target=\"_blank\" rel=\"noopener\"><strong>[SOLUTIO]<\/strong><\/a><\/li>\n<li>Nummus in puteum deicitur. Sonus qui indicat nummum ad fundum pervenisse post 10 [s] auditur. Quae est profunditas putei? <a href=\"https:\/\/www.youtube.com\/watch?v=P21bsNFF9Fw&amp;t=1972s\" target=\"_blank\" rel=\"noopener\"><strong>[SOLUTIO]<\/strong><\/a><\/li>\n<li>Homo verticaliter in caelum spuit et in 1.2[s] in faciem suam redit. a) Qua velocitate sputum misit? b) Quam altitudinem sputum attigit? <a href=\"https:\/\/www.youtube.com\/watch?v=P21bsNFF9Fw&amp;t=2090s\" target=\"_blank\" rel=\"noopener\"><strong>[SOLUTIO]<\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Motus Rectilineus Uniformiter Acceleratus (MRUA) Summarium: In hac lectione recognoscemus notionem motus rectilinei uniformiter accelerati (MRUA). Explicabitur quomodo hic motus accelerationem constantem in linea recta implicet et per aequationes ex integratione obtentas exprimatur. Proposita Discendi: Huius lectionis fine, discipulus poterit: Intelligere notionem motus rectilinei uniformiter accelerati (MRUA) eiusque proprietates. Deducere aequationes itineris pro MRUA ex [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28458,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":100,"footnotes":""},"categories":[1262,1250],"tags":[],"class_list":["post-34449","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fundamenta-mechanicae","category-physica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Motus Rectilineus Uniformiter Acceleratus (MRUA) - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Motus rectilineus uniformiter acceleratus (MRUA) est motus in linea recta ubi obiectum accelerationem constantem tempore experitur\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformiter-acceleratus-mrua\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Motus Rectilineus Uniformiter Acceleratus (MRUA)\" \/>\n<meta property=\"og:description\" content=\"Motus rectilineus uniformiter acceleratus (MRUA) est motus in linea recta ubi obiectum accelerationem constantem tempore experitur\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformiter-acceleratus-mrua\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-09-08T13:00:31+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-08T03:26:52+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/aceleracion-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Motus Rectilineus Uniformiter Acceleratus (MRUA)\" \/>\n<meta name=\"twitter:description\" content=\"Motus rectilineus uniformiter acceleratus (MRUA) est motus in linea recta ubi obiectum accelerationem constantem tempore experitur\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/aceleracion.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformiter-acceleratus-mrua\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformiter-acceleratus-mrua\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Motus Rectilineus Uniformiter Acceleratus (MRUA)\",\"datePublished\":\"2021-09-08T13:00:31+00:00\",\"dateModified\":\"2025-09-08T03:26:52+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformiter-acceleratus-mrua\/\"},\"wordCount\":714,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformiter-acceleratus-mrua\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/aceleracion.jpg\",\"articleSection\":[\"Fundamenta Mechanicae\",\"Physica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformiter-acceleratus-mrua\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformiter-acceleratus-mrua\/\",\"url\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformiter-acceleratus-mrua\/\",\"name\":\"Motus Rectilineus Uniformiter Acceleratus (MRUA) - 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