{"id":28445,"date":"2021-09-03T13:00:56","date_gmt":"2021-09-03T13:00:56","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28445"},"modified":"2024-09-16T11:44:53","modified_gmt":"2024-09-16T11:44:53","slug":"mouvement-rectiligne-uniforme-m-r-u","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/fr\/mouvement-rectiligne-uniforme-m-r-u\/","title":{"rendered":"Mouvement Rectiligne Uniforme (M.R.U.)"},"content":{"rendered":"<p><center><\/p>\n<h1>Mouvement Rectiligne Uniforme (M.R.U.)<\/h1>\n<p><\/center><br \/>\n<center><em><strong>R\u00e9sum\u00e9 :<\/strong><\/p>\n<p>Dans ce cours, nous nous concentrerons sur l&#8217;application des \u00e9quations au mouvement rectiligne uniforme, essentiel pour comprendre comment les objets se d\u00e9placent \u00e0 vitesse constante. Nous r\u00e9viserons les \u00e9quations sur l&#8217;axe <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> et verrons leur simplification lorsque l&#8217;acc\u00e9l\u00e9ration est nulle, ce qui nous permettra de calculer la position d&#8217;un mobile en connaissant sa vitesse et sa position initiale. Enfin, nous appliquerons ces concepts avec des exemples et des exercices pratiques.<\/p>\n<p><\/em><br \/>\n<\/center><\/p>\n<p><center><strong><u>Objectifs d&#8217;apprentissage<\/u><\/strong><\/p>\n<p>\u00c0 la fin de ce cours, on s&#8217;attend \u00e0 ce que l&#8217;\u00e9tudiant soit capable de :<\/p>\n<p><\/center><\/p>\n<ol>\n<li><strong>Comprendre<\/strong> les \u00e9quations de trajectoire : Reconna\u00eetre et comprendre les \u00e9quations de mouvement, en particulier pour l&#8217;axe <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span>, et leur application dans la description du mouvement des corps.<\/li>\n<li><strong>Appliquer<\/strong> les \u00e9quations au mouvement rectiligne uniforme : Apprendre \u00e0 simplifier les \u00e9quations de trajectoire lorsque l&#8217;acc\u00e9l\u00e9ration est nulle, pour d\u00e9crire le mouvement rectiligne uniforme.<\/li>\n<li><strong>Identifier<\/strong> les caract\u00e9ristiques du mouvement rectiligne uniforme : Savoir que dans ce type de mouvement, la direction et la vitesse de l&#8217;objet restent constantes.<\/li>\n<li><strong>Calculer<\/strong> la position d&#8217;un mobile : Utiliser les \u00e9quations de mouvement pour d\u00e9terminer la position d&#8217;un objet \u00e0 tout instant, \u00e9tant donn\u00e9 sa position et sa vitesse initiales.<\/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>Les \u00e9quations de trajectoire du M.R.U.<\/h2>\n<p style=\"text-align: justify;\">Dans le <a href=\"http:\/\/toposuranos.com\/material\/es\/cinematica\/\" rel=\"noopener\" target=\"_blank\">cours pr\u00e9c\u00e9dent<\/a>, nous avons revu les raisonnements qui conduisent aux \u00e9quations de trajectoire pour la description du mouvement des corps. Il est maintenant temps de les mettre dans le contexte de certains ph\u00e9nom\u00e8nes simples pour commencer \u00e0 pratiquer. Le plus simple de ces ph\u00e9nom\u00e8nes correspond au mouvement rectiligne uniforme.<\/p>\n<p style=\"text-align: justify;\">Avant de continuer, rappelons la forme des \u00e9quations de trajectoire. Pour l&#8217;axe de coordonn\u00e9es <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span>, elles sont :<\/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;\">Ici, <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> repr\u00e9sentent l&#8217;acc\u00e9l\u00e9ration, la vitesse et la position initiale du mobile, <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> sont l&#8217;acc\u00e9l\u00e9ration, la vitesse et la position du mobile en fonction du temps, respectivement. Toutes ces expressions sont \u00e9crites de mani\u00e8re analogue pour les autres axes de coordonn\u00e9es <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{z}<\/span>, pour repr\u00e9senter le mouvement dans 1, 2 et 3 dimensions spatiales.<\/p>\n<h2>Contextualisation du mouvement rectiligne uniforme<\/h2>\n<p style=\"text-align: justify;\">Pour placer les \u00e9quations de trajectoire dans le contexte du mouvement rectiligne uniforme, nous devons r\u00e9pondre \u00e0 la question : Qu&#8217;est-ce qu&#8217;un mouvement rectiligne uniforme ? et transformer cette question en conditions que nous pouvons imposer aux \u00e9quations de trajectoire :<\/p>\n<ul style=\"text-align: justify;\">\n<li>La direction du mouvement ne change pas avec le temps<\/li>\n<li>la vitesse du mouvement ne change pas non plus<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">Tout cela se r\u00e9sume \u00e0 \u00e9tablir que l&#8217;acc\u00e9l\u00e9ration dans les trois axes est nulle \u00e0 tout instant ; et avec cela, les \u00e9quations de trajectoire sont les suivantes :<\/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 de mani\u00e8re analogue pour les autres axes. Avec cela, en connaissant la position et la vitesse initiales, il est possible de d\u00e9terminer la position du mobile \u00e0 tout instant.<\/p>\n<p style=\"text-align: justify;\">En utilisant ces \u00e9quations et en partant des conditions initiales pour la position et la vitesse, il est possible de d\u00e9terminer la position du mobile \u00e0 tout instant.<\/p>\n<h2>Exercices d&#8217;exemple :<\/h2>\n<ol style=\"text-align: justify;\">\n<li>Trouvez la position \u00e0 l&#8217;instant <span class=\"katex-eq\" data-katex-display=\"false\">t=15[s]<\/span> d&#8217;un mobile dont la position et la vitesse initiales sont donn\u00e9es ci-dessous :\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>Deux trains sont initialement s\u00e9par\u00e9s par une distance de 10 kilom\u00e8tres. Les deux se d\u00e9placent sur la m\u00eame ligne de rails ; le premier \u00e0 une vitesse de <span class=\"katex-eq\" data-katex-display=\"false\">v_{1}=20[km\/h]<\/span>, et le second \u00e0 une vitesse de <span class=\"katex-eq\" data-katex-display=\"false\">v_2=15[km\/h]<\/span> mais en sens inverse.\n<ol>\n<li type=\"a\">Combien de temps les trains mettent-ils pour se percuter ?<\/a>\n<li type=\"a\">Quelle distance parcourt chaque train depuis sa position initiale jusqu&#8217;au point d&#8217;impact ?<\/a>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Mouvement Rectiligne Uniforme (M.R.U.) R\u00e9sum\u00e9 : Dans ce cours, nous nous concentrerons sur l&#8217;application des \u00e9quations au mouvement rectiligne uniforme, essentiel pour comprendre comment les objets se d\u00e9placent \u00e0 vitesse constante. Nous r\u00e9viserons les \u00e9quations sur l&#8217;axe et verrons leur simplification lorsque l&#8217;acc\u00e9l\u00e9ration est nulle, ce qui nous permettra de calculer la position d&#8217;un mobile [&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":35,"footnotes":""},"categories":[663,647],"tags":[],"class_list":["post-28445","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fondements-de-la-mecanique","category-physique"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Mouvement Rectiligne Uniforme (M.R.U.) - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Le mouvement rectiligne uniforme est celui dans lequel un objet se d\u00e9place en ligne droite \u00e0 une vitesse constante, sans changements.\" \/>\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\/fr\/mouvement-rectiligne-uniforme-m-r-u\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mouvement Rectiligne Uniforme (M.R.U.)\" \/>\n<meta property=\"og:description\" content=\"Le mouvement rectiligne uniforme est celui dans lequel un objet se d\u00e9place en ligne droite \u00e0 une vitesse constante, sans changements.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/fr\/mouvement-rectiligne-uniforme-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=\"2021-09-03T13:00:56+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-16T11:44:53+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=\"Mouvement Rectiligne Uniforme (M.R.U.)\" \/>\n<meta name=\"twitter:description\" content=\"Le mouvement rectiligne uniforme est celui dans lequel un objet se d\u00e9place en ligne droite \u00e0 une vitesse constante, sans changements.\" \/>\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=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/mouvement-rectiligne-uniforme-m-r-u\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/mouvement-rectiligne-uniforme-m-r-u\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Mouvement Rectiligne Uniforme (M.R.U.)\",\"datePublished\":\"2021-09-03T13:00:56+00:00\",\"dateModified\":\"2024-09-16T11:44:53+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/mouvement-rectiligne-uniforme-m-r-u\/\"},\"wordCount\":724,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/mouvement-rectiligne-uniforme-m-r-u\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg\",\"articleSection\":[\"Fondements de la M\u00e9canique\",\"Physique\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/fr\/mouvement-rectiligne-uniforme-m-r-u\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/fr\/mouvement-rectiligne-uniforme-m-r-u\/\",\"url\":\"http:\/\/toposuranos.com\/material\/fr\/mouvement-rectiligne-uniforme-m-r-u\/\",\"name\":\"Mouvement Rectiligne Uniforme (M.R.U.) - 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