{"id":28441,"date":"2021-09-03T13:00:56","date_gmt":"2021-09-03T13:00:56","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28441"},"modified":"2024-09-16T11:46:23","modified_gmt":"2024-09-16T11:46:23","slug":"%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/","title":{"rendered":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.)"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.)<\/h1>\n<p><\/center><br \/>\n<center><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><\/p>\n<p>\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0915\u0947 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 \u0915\u093f \u0935\u0938\u094d\u0924\u0941\u090f\u0902 \u0938\u094d\u0925\u093f\u0930 \u0935\u0947\u0917 \u0938\u0947 \u0915\u0948\u0938\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0902\u0964 \u0939\u092e <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> \u0905\u0915\u094d\u0937 \u092a\u0930 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u091c\u092c \u0924\u094d\u0935\u0930\u0923 \u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948 \u0924\u094b \u0909\u0928\u0915\u093e \u0938\u0930\u0932\u0940\u0915\u0930\u0923 \u0915\u0948\u0938\u0947 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u0915\u093f\u0938\u0940 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0917\u0924\u093f \u0914\u0930 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u091c\u093e\u0928\u0928\u0947 \u092a\u0930 \u0909\u0938\u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0964 \u0905\u0902\u0924 \u092e\u0947\u0902, \u0939\u092e \u0907\u0928 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u0909\u0926\u093e\u0939\u0930\u0923\u094b\u0902 \u0914\u0930 \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0905\u092d\u094d\u092f\u093e\u0938\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0932\u093e\u0917\u0942 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/p>\n<p><\/em><br \/>\n<\/center><\/p>\n<p><center><strong><u>\u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/u><\/strong><\/p>\n<p>\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926, \u092f\u0939 \u0905\u092a\u0947\u0915\u094d\u0937\u093e \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u0915\u093f \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947:<\/p>\n<p><\/center><\/p>\n<ol>\n<li><strong>\u0938\u092e\u091d\u0947\u0902<\/strong> \u092a\u0925 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b: \u0917\u0924\u093f \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u092a\u0939\u091a\u093e\u0928\u0947\u0902 \u0914\u0930 \u0938\u092e\u091d\u0947\u0902, \u0935\u093f\u0936\u0947\u0937\u0915\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> \u0905\u0915\u094d\u0937 \u0915\u0947 \u0932\u093f\u090f, \u0914\u0930 \u0909\u0928\u094d\u0939\u0947\u0902 \u0935\u0938\u094d\u0924\u0941\u0913\u0902 \u0915\u0940 \u0917\u0924\u093f \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0915\u0948\u0938\u0947 \u0932\u093e\u0917\u0942 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0964<\/li>\n<li><strong>\u0932\u093e\u0917\u0942 \u0915\u0930\u0947\u0902<\/strong> \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u092a\u0930: \u092f\u0939 \u0938\u0940\u0916\u0947\u0902 \u0915\u093f \u091c\u092c \u0924\u094d\u0935\u0930\u0923 \u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948 \u0924\u094b \u092a\u0925 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u0938\u0930\u0932 \u0915\u0948\u0938\u0947 \u0915\u093f\u092f\u093e \u091c\u093e\u090f, \u0924\u093e\u0915\u093f \u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947\u0964<\/li>\n<li><strong>\u092a\u0939\u091a\u093e\u0928\u0947\u0902<\/strong> \u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0902: \u091c\u093e\u0928\u0947\u0902 \u0915\u093f \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0940 \u0917\u0924\u093f \u092e\u0947\u0902, \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0926\u093f\u0936\u093e \u0914\u0930 \u0917\u0924\u093f \u0938\u094d\u0925\u093f\u0930 \u0930\u0939\u0924\u0940 \u0939\u0948\u0902\u0964<\/li>\n<li><strong>\u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902<\/strong> \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f: \u0917\u0924\u093f \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0915\u093f\u0938\u0940 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u094b \u0915\u093f\u0938\u0940 \u092d\u0940 \u0915\u094d\u0937\u0923 \u092e\u0947\u0902 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0947\u0902, \u0909\u0938\u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u0914\u0930 \u0917\u0924\u093f \u0915\u094b \u091c\u093e\u0928\u0915\u0930\u0964<\/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>\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0915\u0947 \u092a\u0925 \u0938\u092e\u0940\u0915\u0930\u0923<\/h2>\n<p style=\"text-align: justify;\">\u092a\u093f\u091b\u0932\u0940 <a href=\"http:\/\/toposuranos.com\/material\/es\/cinematica\/\" rel=\"noopener\" target=\"_blank\">\u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902<\/a> \u0939\u092e\u0928\u0947 \u0909\u0928 \u0924\u0930\u094d\u0915\u094b\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u091c\u094b \u0935\u0938\u094d\u0924\u0941\u0913\u0902 \u0915\u0940 \u0917\u0924\u093f \u0915\u0947 \u0935\u0930\u094d\u0923\u0928 \u0915\u0947 \u0932\u093f\u090f \u092a\u0925 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0940 \u0913\u0930 \u0932\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0905\u092c \u0938\u092e\u092f \u0939\u0948 \u0915\u093f \u0939\u092e \u0909\u0928\u094d\u0939\u0947\u0902 \u0915\u0941\u091b \u0938\u0930\u0932 \u0918\u091f\u0928\u093e\u0913\u0902 \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u0930\u0916\u0947\u0902 \u0924\u093e\u0915\u093f \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930\u0928\u093e \u0936\u0941\u0930\u0942 \u0915\u0930 \u0938\u0915\u0947\u0902\u0964 \u0907\u0928 \u0918\u091f\u0928\u093e\u0913\u0902 \u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u0938\u0930\u0932 \u0939\u0948 \u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928\u0964<\/p>\n<p style=\"text-align: justify;\">\u0906\u0917\u0947 \u092c\u0922\u093c\u0928\u0947 \u0938\u0947 \u092a\u0939\u0932\u0947, \u091a\u0932\u093f\u090f \u092a\u0925 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u0930\u0942\u092a \u0915\u094b \u092f\u093e\u0926 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0938\u092e\u0928\u094d\u0935\u092f \u0905\u0915\u094d\u0937 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span> \u0915\u0947 \u0932\u093f\u090f, \u092f\u0947 \u0938\u092e\u0940\u0915\u0930\u0923 \u0939\u0948\u0902:<\/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;\">\u092f\u0939\u093e\u0902, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_{0x}, v_{0x}<\/span><\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0924\u094d\u0935\u0930\u0923, \u0935\u0947\u0917 \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_x(t), v_x(t)<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x(t)<\/span><\/span> \u0915\u094d\u0930\u092e\u0936\u0903 \u0938\u092e\u092f \u092a\u0930 \u0935\u0938\u094d\u0924\u0941 \u0915\u093e \u0924\u094d\u0935\u0930\u0923, \u0935\u0947\u0917 \u0914\u0930 \u0938\u094d\u0925\u093f\u0924\u093f \u0939\u0948\u0902\u0964 \u092f\u0947 \u0938\u092d\u0940 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f\u092f\u093e\u0902 \u0905\u0928\u094d\u092f \u0938\u092e\u0928\u094d\u0935\u092f \u0905\u0915\u094d\u0937\u094b\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{y}<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\hat{z}<\/span> \u0915\u0947 \u0932\u093f\u090f \u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902, \u0924\u093e\u0915\u093f 1, 2 \u0914\u0930 3 \u0906\u092f\u093e\u092e\u0940 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u092e\u0947\u0902 \u0917\u0924\u093f \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947\u0964<\/p>\n<h2>\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0915\u093e \u0938\u0902\u0926\u0930\u094d\u092d<\/h2>\n<p style=\"text-align: justify;\">\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u092a\u0925 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u094b \u0930\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u0936\u094d\u0928 \u0915\u093e \u0909\u0924\u094d\u0924\u0930 \u0926\u0947\u0928\u093e \u0939\u094b\u0917\u093e: \u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0915\u094d\u092f\u093e \u0939\u0948? \u0914\u0930 \u0909\u0938 \u092a\u094d\u0930\u0936\u094d\u0928 \u0915\u094b \u0910\u0938\u0940 \u0936\u0930\u094d\u0924\u094b\u0902 \u092e\u0947\u0902 \u092c\u0926\u0932\u0928\u093e \u0939\u094b\u0917\u093e \u091c\u093f\u0938\u0947 \u0939\u092e \u092a\u0925 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u092a\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930 \u0938\u0915\u0947\u0902:<\/p>\n<ul style=\"text-align: justify;\">\n<li>\u0917\u0924\u093f \u0915\u0940 \u0926\u093f\u0936\u093e \u0938\u092e\u092f \u0915\u0947 \u0938\u093e\u0925 \u0928\u0939\u0940\u0902 \u092c\u0926\u0932\u0924\u0940 \u0939\u0948<\/li>\n<li>\u0917\u0924\u093f \u0915\u0940 \u0917\u0924\u093f \u092d\u0940 \u0928\u0939\u0940\u0902 \u092c\u0926\u0932\u0924\u0940<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u092f\u0939 \u0938\u092c \u0924\u0940\u0928\u094b\u0902 \u0905\u0915\u094d\u0937\u094b\u0902 \u092e\u0947\u0902 \u0924\u094d\u0935\u0930\u0923 \u0915\u094b \u0939\u0930 \u0938\u092e\u092f \u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0928\u0947 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0915\u0947 \u0938\u0902\u0915\u094d\u0937\u0947\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948; \u0914\u0930 \u0907\u0938\u0915\u0947 \u0938\u093e\u0925, \u092a\u0925 \u0938\u092e\u0940\u0915\u0930\u0923 \u0907\u0938 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902:<\/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;\">\u0914\u0930 \u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 \u0905\u0928\u094d\u092f \u0905\u0915\u094d\u0937\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f\u0964 \u0907\u0938\u0915\u0947 \u0938\u093e\u0925, \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u0914\u0930 \u0917\u0924\u093f \u0915\u094b \u091c\u093e\u0928\u0924\u0947 \u0939\u0941\u090f, \u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u092e\u092f \u092e\u0947\u0902 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p style=\"text-align: justify;\">\u0907\u0928 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0914\u0930 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u0914\u0930 \u0917\u0924\u093f \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f, \u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u092e\u092f \u092a\u0930 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0964<\/p>\n<h2>\u0909\u0926\u093e\u0939\u0930\u0923 \u0905\u092d\u094d\u092f\u093e\u0938:<\/h2>\n<ol style=\"text-align: justify;\">\n<li>\u0938\u092e\u092f <span class=\"katex-eq\" data-katex-display=\"false\">t=15[s]<\/span> \u092a\u0930 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u0915\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902 \u091c\u093f\u0938\u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u0914\u0930 \u0917\u0924\u093f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u0948:\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>\u0926\u094b \u091f\u094d\u0930\u0947\u0928\u0947\u0902 \u0936\u0941\u0930\u0942 \u092e\u0947\u0902 10 \u0915\u093f\u0932\u094b\u092e\u0940\u091f\u0930 \u0915\u0940 \u0926\u0942\u0930\u0940 \u092a\u0930 \u0939\u0948\u0902\u0964 \u0926\u094b\u0928\u094b\u0902 \u090f\u0915 \u0939\u0940 \u091f\u094d\u0930\u0948\u0915 \u092a\u0930 \u091a\u0932 \u0930\u0939\u0940 \u0939\u0948\u0902; \u092a\u0939\u0932\u0940 \u0915\u0940 \u0917\u0924\u093f <span class=\"katex-eq\" data-katex-display=\"false\">v_{1}=20[km\/h]<\/span> \u0939\u0948, \u0914\u0930 \u0926\u0942\u0938\u0930\u0940 \u0915\u0940 \u0917\u0924\u093f <span class=\"katex-eq\" data-katex-display=\"false\">v_2=15[km\/h]<\/span> \u0939\u0948 \u0932\u0947\u0915\u093f\u0928 \u0935\u093f\u092a\u0930\u0940\u0924 \u0926\u093f\u0936\u093e \u092e\u0947\u0902\u0964\n<ol>\n<li type=\"a\">\u091f\u094d\u0930\u0947\u0928\u094b\u0902 \u0915\u094b \u091f\u0915\u0930\u093e\u0928\u0947 \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u093e \u0938\u092e\u092f \u0932\u0917\u0924\u093e \u0939\u0948?<\/a>\n<li type=\"a\">\u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u0938\u0947 \u091f\u0915\u094d\u0915\u0930 \u092c\u093f\u0902\u0926\u0941 \u0924\u0915 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091f\u094d\u0930\u0947\u0928 \u0915\u093f\u0924\u0928\u0940 \u0926\u0942\u0930\u0940 \u0924\u092f \u0915\u0930\u0924\u0940 \u0939\u0948?<\/a>\n<\/ol>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.) \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0915\u0947 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0947 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917 \u092a\u0930 \u0927\u094d\u092f\u093e\u0928 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 \u0915\u093f \u0935\u0938\u094d\u0924\u0941\u090f\u0902 \u0938\u094d\u0925\u093f\u0930 \u0935\u0947\u0917 \u0938\u0947 \u0915\u0948\u0938\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0902\u0964 \u0939\u092e \u0905\u0915\u094d\u0937 \u092a\u0930 \u0938\u092e\u0940\u0915\u0930\u0923\u094b\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u091c\u092c \u0924\u094d\u0935\u0930\u0923 \u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948 \u0924\u094b \u0909\u0928\u0915\u093e [&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":0,"footnotes":""},"categories":[643,659],"tags":[],"class_list":["post-28441","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-643","category-659"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.) - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0935\u0939 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u090f\u0915 \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0930 \u0935\u0947\u0917 \u0938\u0947 \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0964\" \/>\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\/hi\/\u0938\u092e\u093e\u0928-\u0917\u0924\u093f-\u0914\u0930-\u0930\u0947\u0916\u0940\u092f-\u0938\u0902\u091a\u0932\u0928-m-r-u\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.)\" \/>\n<meta property=\"og:description\" content=\"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0935\u0939 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u090f\u0915 \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0930 \u0935\u0947\u0917 \u0938\u0947 \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0964\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/hi\/\u0938\u092e\u093e\u0928-\u0917\u0924\u093f-\u0914\u0930-\u0930\u0947\u0916\u0940\u092f-\u0938\u0902\u091a\u0932\u0928-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=\"2024-09-16T11:46:23+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=\"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.)\" \/>\n<meta name=\"twitter:description\" content=\"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0935\u0939 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u090f\u0915 \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0930 \u0935\u0947\u0917 \u0938\u0947 \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0964\" \/>\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=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.)\",\"datePublished\":\"2021-09-03T13:00:56+00:00\",\"dateModified\":\"2024-09-16T11:46:23+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/\"},\"wordCount\":134,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg\",\"articleSection\":[\"\u092d\u094c\u0924\u093f\u0915\u0940\",\"\u092e\u0947\u0915\u0948\u0928\u093f\u0915\u094d\u0938 \u0915\u0940 \u092e\u0942\u0932 \u092c\u093e\u0924\u0947\u0902\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/\",\"url\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/\",\"name\":\"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.) - toposuranos.com\/material\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#primaryimage\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg\",\"datePublished\":\"2021-09-03T13:00:56+00:00\",\"dateModified\":\"2024-09-16T11:46:23+00:00\",\"description\":\"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0935\u0939 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u090f\u0915 \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0930 \u0935\u0947\u0917 \u0938\u0947 \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0964\",\"breadcrumb\":{\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#primaryimage\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg\",\"width\":1792,\"height\":1024},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.)\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\/\/toposuranos.com\/material\/#website\",\"url\":\"http:\/\/toposuranos.com\/material\/\",\"name\":\"toposuranos.com\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\/\/toposuranos.com\/material\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\",\"name\":\"toposuranos.com\/material\",\"url\":\"http:\/\/toposuranos.com\/material\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\/material\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/groups\/toposuranos\",\"https:\/\/x.com\/topuranos\",\"https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\/\/www.linkedin.com\/company\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\/\/toposuranos.com\/material\"],\"url\":\"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.) - toposuranos.com\/material","description":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0935\u0939 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u090f\u0915 \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0930 \u0935\u0947\u0917 \u0938\u0947 \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0964","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/hi\/\u0938\u092e\u093e\u0928-\u0917\u0924\u093f-\u0914\u0930-\u0930\u0947\u0916\u0940\u092f-\u0938\u0902\u091a\u0932\u0928-m-r-u\/","og_locale":"es_ES","og_type":"article","og_title":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.)","og_description":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0935\u0939 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u090f\u0915 \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0930 \u0935\u0947\u0917 \u0938\u0947 \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0964","og_url":"http:\/\/toposuranos.com\/material\/hi\/\u0938\u092e\u093e\u0928-\u0917\u0924\u093f-\u0914\u0930-\u0930\u0947\u0916\u0940\u092f-\u0938\u0902\u091a\u0932\u0928-m-r-u\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2021-09-03T13:00:56+00:00","article_modified_time":"2024-09-16T11:46:23+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru-1024x585.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.)","twitter_description":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0935\u0939 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u090f\u0915 \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0930 \u0935\u0947\u0917 \u0938\u0947 \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0964","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"4 minutos"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.)","datePublished":"2021-09-03T13:00:56+00:00","dateModified":"2024-09-16T11:46:23+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/"},"wordCount":134,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg","articleSection":["\u092d\u094c\u0924\u093f\u0915\u0940","\u092e\u0947\u0915\u0948\u0928\u093f\u0915\u094d\u0938 \u0915\u0940 \u092e\u0942\u0932 \u092c\u093e\u0924\u0947\u0902"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/","url":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/","name":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.) - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg","datePublished":"2021-09-03T13:00:56+00:00","dateModified":"2024-09-16T11:46:23+00:00","description":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 \u0935\u0939 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u090f\u0915 \u0935\u0938\u094d\u0924\u0941 \u090f\u0915 \u0938\u0940\u0927\u0940 \u0930\u0947\u0916\u093e \u092e\u0947\u0902 \u0938\u094d\u0925\u093f\u0930 \u0935\u0947\u0917 \u0938\u0947 \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u091a\u0932\u0924\u0940 \u0939\u0948\u0964","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2021\/09\/mru.jpg","width":1792,"height":1024},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%97%e0%a4%a4%e0%a4%bf-%e0%a4%94%e0%a4%b0-%e0%a4%b0%e0%a5%87%e0%a4%96%e0%a5%80%e0%a4%af-%e0%a4%b8%e0%a4%82%e0%a4%9a%e0%a4%b2%e0%a4%a8-m-r-u\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0938\u092e\u093e\u0928 \u0917\u0924\u093f \u0914\u0930 \u0930\u0947\u0916\u0940\u092f \u0938\u0902\u091a\u0932\u0928 (M.R.U.)"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/28441","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=28441"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/28441\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/28430"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=28441"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=28441"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=28441"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}