{"id":34437,"date":"2021-09-03T13:00:00","date_gmt":"2021-09-03T13:00:00","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34437"},"modified":"2025-09-08T03:19:27","modified_gmt":"2025-09-08T03:19:27","slug":"motus-rectilineus-uniformisque-m-r-u","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformisque-m-r-u\/","title":{"rendered":"Motus Rectilineus Uniformisque (M.R.U.)"},"content":{"rendered":"<p><center><\/p>\n<h1>Motus Rectilineus Uniformisque (M.R.U.)<\/h1>\n<p><\/center><br \/>\n<center><em><strong>Summarium:<\/strong><\/p>\n<p>In hac lectione intendemus adhibere aequationes motui rectilineo uniformi, quod est fundamentale ad intellegendum quomodo corpora constantia velocitate moveantur. Recognoscemus aequationes in axe <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> atque videbimus earum simplificationem cum acceleratio nulla est, quod sinit nos positionem mobilis computare cognita velocitate et positione initiali. Postremo hos conceptus applicabimus cum exemplis et exercitationibus practicis.<\/p>\n<p><\/em><br \/>\n<\/center><\/p>\n<p><center><strong><u>Proposita Discendi<\/u><\/strong><\/p>\n<p>Completa hac lectione exspectatur discipulum posse:<\/p>\n<p><\/center><\/p>\n<ol>\n<li><strong>Intellegere<\/strong> aequationes itinerarii: Cognoscere atque intellegere aequationes motus, praesertim pro axe <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span>, earumque applicationem in descriptione motus corporum.<\/li>\n<li><strong>Applicare<\/strong> aequationes motui rectilineo uniformi: Discere simplificare aequationes itinerarii cum acceleratio nulla est, ut describatur motus rectilineus et uniformis.<\/li>\n<li><strong>Identificare<\/strong> notas motus rectilinei uniformis: Scire in hoc genere motus directionem et celeritatem corporis constantes manere.<\/li>\n<li><strong>Computare<\/strong> positionem mobilis: Uti aequationibus motus ad determinandam positionem obiecti in quolibet tempore, data eius positione et velocitate initiali.<\/li>\n<\/ol>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/_bLJLf9dNfY\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<h2>Aequationes itinerarii M.R.U.<\/h2>\n<p style=\"text-align: justify;\">In <a href=\"http:\/\/toposuranos.com\/material\/es\/cinematica\/\" rel=\"noopener\" target=\"_blank\">praecedenti lectione<\/a> recognovimus rationes quae ducunt ad aequationes itinerarii ad descriptionem motus corporum, nunc autem oportet eas ponere in contextu quorumdam phaenomenorum simplicium ad incipiendum exercitium. Facillimum horum phaenomenorum respondet motui rectilineo et uniformi.<\/p>\n<p style=\"text-align: justify;\">Antequam pergamus, meminerimus formam aequationum itinerarii. Pro axe coordinato <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> hae sunt:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><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; a_{0x}t+v_{0x}\\\\ \\\\\n\nx(t) &amp; = &amp; \\frac{1}{2}a_{0x}t^2 + v_{0x}t + x_0\n\n\\end{array}\n\n<\/span><\/span><\/p>\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 class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> repraesentant accelerationem, velocitatem et positionem initialem mobilis, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_x(t), v_x(t)<\/span><\/span> et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x(t)<\/span><\/span> sunt acceleratio, velocitas et positio mobilis tempore, respective. Omnes hae formulae scribuntur similiter pro reliquis axibus coordinatis <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{z}<\/span>, ad repraesentandum motum in 1, 2 et 3 dimensionibus spatii.<\/p>\n<h2>Contextualizatio motus rectilinei uniformisque<\/h2>\n<p style=\"text-align: justify;\">Ut aequationes itinerarii ponamus in contextu motus rectilinei uniformis, necesse est respondere quaestioni: Quid est motus rectilineus et uniformis? atque hanc quaestionem vertere in condiciones quas aequationibus itinerarii imponere possimus:<\/p>\n<ul style=\"text-align: justify;\">\n<li>Directio motus non mutatur tempore<\/li>\n<li>celeritas quoque motus non mutatur<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Hoc totum colligitur statuendo accelerationem in tribus axibus nullam esse omni momento; atque ita aequationes itinerarii hunc in modum redeunt:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rcl}\n\nv_x(t) &amp; = &amp; v_{0x}\\\\ \\\\\n\nx(t) &amp; = &amp; v_{0x}t + x_0\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Et similiter pro reliquis axibus. Hoc modo, cognita positione et velocitate initiali, fieri potest determinare positionem mobilis in quolibet temporis momento.<\/p>\n<p style=\"text-align: justify;\">His aequationibus utens et ex condicionibus initialibus pro positione et velocitate, fieri potest determinare positionem mobilis in quolibet temporis momento.<\/p>\n<h2>Exercitia exemplaria:<\/h2>\n<ol style=\"text-align: justify;\">\n<li>Inveni positionem in momento <span class=\"katex-eq\" data-katex-display=\"false\">t=15[s]<\/span> mobilis cuius positio et velocitas initialis infra data sunt:\n<ol>\n<li type=\"a\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_{0x}=0,25[m\/s]\\;\\;x_0=0,3[m]<\/span><\/span><\/li>\n<li type=\"a\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_{0x}=10[km\/h]\\;\\;x_0=15[m]<\/span><\/span><\/li>\n<li type=\"a\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_{0x}=-3[m\/min]\\;\\;x_0=4[in]<\/span><\/span><\/li>\n<\/ol>\n<\/li>\n<li>Duae tramina initio distantia 10 chiliometrorum separantur. Utraque per eandem lineam ursorum moventur; primum celeritate <span class=\"katex-eq\" data-katex-display=\"false\">v_{1}=20[km\/h]<\/span>, alterum celeritate <span class=\"katex-eq\" data-katex-display=\"false\">v_2=15[km\/h]<\/span> sed in partem contrariam.\n<ol>\n<li type=\"a\">Quanto tempore tramina colliduntur?<\/a>\n<li type=\"a\">Quam distantiam quodque tramen a sua positione initiali usque ad locum impactus percurrit?<\/a>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Motus Rectilineus Uniformisque (M.R.U.) Summarium: In hac lectione intendemus adhibere aequationes motui rectilineo uniformi, quod est fundamentale ad intellegendum quomodo corpora constantia velocitate moveantur. Recognoscemus aequationes in axe atque videbimus earum simplificationem cum acceleratio nulla est, quod sinit nos positionem mobilis computare cognita velocitate et positione initiali. Postremo hos conceptus applicabimus cum exemplis et exercitationibus [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28430,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":134,"footnotes":""},"categories":[1262,1250],"tags":[],"class_list":["post-34437","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 Uniformisque (M.R.U.) - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Motus rectilineus uniformis est is in quo obiectum linea recta ad velocitatem constantem, sine mutationibus, movetur.\" \/>\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-uniformisque-m-r-u\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Motus Rectilineus Uniformisque (M.R.U.)\" \/>\n<meta property=\"og:description\" content=\"Motus rectilineus uniformis est is in quo obiectum linea recta ad velocitatem constantem, sine mutationibus, movetur.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformisque-m-r-u\/\" \/>\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=\"2021-09-03T13:00:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-08T03:19:27+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru-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 Uniformisque (M.R.U.)\" \/>\n<meta name=\"twitter:description\" content=\"Motus rectilineus uniformis est is in quo obiectum linea recta ad velocitatem constantem, sine mutationibus, movetur.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.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-uniformisque-m-r-u\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformisque-m-r-u\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Motus Rectilineus Uniformisque (M.R.U.)\",\"datePublished\":\"2021-09-03T13:00:00+00:00\",\"dateModified\":\"2025-09-08T03:19:27+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformisque-m-r-u\/\"},\"wordCount\":514,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformisque-m-r-u\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg\",\"articleSection\":[\"Fundamenta Mechanicae\",\"Physica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformisque-m-r-u\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformisque-m-r-u\/\",\"url\":\"http:\/\/toposuranos.com\/material\/la\/motus-rectilineus-uniformisque-m-r-u\/\",\"name\":\"Motus Rectilineus Uniformisque (M.R.U.) - 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