{"id":28433,"date":"2021-09-03T13:00:58","date_gmt":"2021-09-03T13:00:58","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28433"},"modified":"2024-09-16T11:45:41","modified_gmt":"2024-09-16T11:45:41","slug":"rectilinear-uniform-motion-r-u-m","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/en\/rectilinear-uniform-motion-r-u-m\/","title":{"rendered":"Rectilinear Uniform Motion (R.U.M.)"},"content":{"rendered":"<p><center><\/p>\n<h1>Rectilinear Uniform Motion (R.U.M.)<\/h1>\n<p><\/center><br \/>\n<center><em><strong>Summary:<\/strong><\/p>\n<p>In this class, we will focus on applying the equations to rectilinear uniform motion, which is essential to understand how objects move at a constant speed. We will review the equations on the <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> axis and see their simplification when the acceleration is zero, allowing us to calculate the position of a mobile given its speed and initial position. Finally, we will apply these concepts with examples and practical exercises.<\/p>\n<p><\/em><br \/>\n<\/center><\/p>\n<p><center><strong><u>Learning Objectives<\/u><\/strong><\/p>\n<p>Upon completing this class, the student is expected to:<\/p>\n<p><\/center><\/p>\n<ol>\n<li><strong>Understand<\/strong> the itinerary equations: Recognize and understand the equations of motion, especially for the <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> axis, and their application in describing the motion of bodies.<\/li>\n<li><strong>Apply<\/strong> the equations to rectilinear uniform motion: Learn to simplify the itinerary equations when acceleration is zero, to describe rectilinear uniform motion.<\/li>\n<li><strong>Identify<\/strong> the characteristics of rectilinear uniform motion: Know that in this type of motion, the direction and speed of the object remain constant.<\/li>\n<li><strong>Calculate<\/strong> the position of a mobile: Use the equations of motion to determine the position of an object at any time, given its initial position and speed.<\/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>The Itinerary Equations of R.U.M.<\/h2>\n<p style=\"text-align: justify;\">In the <a href=\"http:\/\/toposuranos.com\/material\/es\/cinematica\/\" rel=\"noopener\" target=\"_blank\">previous class<\/a> we reviewed the reasoning that leads to the itinerary equations for describing the motion of bodies. Now it&#8217;s time to put them in the context of some simple phenomena to start practicing. The simplest of these phenomena corresponds to rectilinear uniform motion.<\/p>\n<p style=\"text-align: justify;\">Before continuing, let&#8217;s recall the form of the itinerary equations. For the coordinate axis <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> these are:<\/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;\">Here, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_{0x}, v_{0x}<\/span><\/span>, and <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> represent the acceleration, speed, and initial position of the mobile, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_x(t), v_x(t)<\/span><\/span>, and <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x(t)<\/span><\/span> are the acceleration, speed, and position of the mobile over time, respectively. All these expressions are written similarly for the other coordinate axes <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{z}<\/span> to represent movement in 1, 2, and 3 spatial dimensions.<\/p>\n<h2>Contextualizing Rectilinear Uniform Motion<\/h2>\n<p style=\"text-align: justify;\">To place the itinerary equations in the context of rectilinear uniform motion, we must answer the question: What is rectilinear uniform motion? and transform that question into conditions that we can impose on the itinerary equations:<\/p>\n<ul style=\"text-align: justify;\">\n<li>The direction of motion does not change over time<\/li>\n<li>nor does the speed of motion change<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">All this is summarized by establishing that the acceleration in the three axes is zero at all times; with this, the itinerary equations are as follows:<\/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;\">And similarly for the other axes. Knowing the initial position and speed, it is possible to determine the position of the mobile at any time.<\/p>\n<p style=\"text-align: justify;\">Using these equations and starting from initial conditions for the position and speed, it is possible to determine the position of the mobile at any time.<\/p>\n<h2>Example Exercises:<\/h2>\n<ol style=\"text-align: justify;\">\n<li>Find the position at the instant <span class=\"katex-eq\" data-katex-display=\"false\">t=15[s]<\/span> of a mobile with the initial position and speed given below:\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>Two trains are initially separated by a distance of 10 kilometers. Both move along the same track; the first with speed <span class=\"katex-eq\" data-katex-display=\"false\">v_{1}=20[km\/h]<\/span>, and the second with speed <span class=\"katex-eq\" data-katex-display=\"false\">v_2=15[km\/h]<\/span> but in the opposite direction.\n<ol>\n<li type=\"a\">How long do the trains take to collide?<\/a>\n<li type=\"a\">What distance does each train cover from its initial position to the point of impact?<\/a>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Rectilinear Uniform Motion (R.U.M.) Summary: In this class, we will focus on applying the equations to rectilinear uniform motion, which is essential to understand how objects move at a constant speed. We will review the equations on the axis and see their simplification when the acceleration is zero, allowing us to calculate the position of [&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":13,"footnotes":""},"categories":[651,635],"tags":[],"class_list":["post-28433","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fundamentals-of-mechanics","category-physics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Rectilinear Uniform Motion (R.U.M.) - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Rectilinear uniform motion is when an object moves in a straight line at a constant speed, without changes.\" \/>\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\/en\/rectilinear-uniform-motion-r-u-m\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rectilinear Uniform Motion (R.U.M.)\" \/>\n<meta property=\"og:description\" content=\"Rectilinear uniform motion is when an object moves in a straight line at a constant speed, without changes.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/en\/rectilinear-uniform-motion-r-u-m\/\" \/>\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=\"2021-09-03T13:00:58+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-16T11:45:41+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=\"Rectilinear Uniform Motion (R.U.M.)\" \/>\n<meta name=\"twitter:description\" content=\"Rectilinear uniform motion is when an object moves in a straight line at a constant speed, without changes.\" \/>\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\\\/en\\\/rectilinear-uniform-motion-r-u-m\\\/#article\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/rectilinear-uniform-motion-r-u-m\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Rectilinear Uniform Motion (R.U.M.)\",\"datePublished\":\"2021-09-03T13:00:58+00:00\",\"dateModified\":\"2024-09-16T11:45:41+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/rectilinear-uniform-motion-r-u-m\\\/\"},\"wordCount\":637,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/rectilinear-uniform-motion-r-u-m\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2021\\\/09\\\/mru.jpg\",\"articleSection\":[\"Fundamentals of Mechanics\",\"Physics\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/rectilinear-uniform-motion-r-u-m\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/rectilinear-uniform-motion-r-u-m\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/en\\\/rectilinear-uniform-motion-r-u-m\\\/\",\"name\":\"Rectilinear Uniform Motion (R.U.M.) - 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