{"id":439,"date":"2017-11-09T16:00:07","date_gmt":"2017-11-09T21:00:07","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1013\/?p=439"},"modified":"2025-12-04T05:52:12","modified_gmt":"2025-12-04T10:52:12","slug":"1eva2009tii_t1-movimiento-particula-plano","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-1eva10\/1eva2009tii_t1-movimiento-particula-plano\/","title":{"rendered":"1Eva2009TII_T1 Movimiento de part\u00edcula en plano"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">1ra Evaluaci\u00f3n II T\u00e9rmino 2009-2010. 1\/Diciembre\/2009. ICM00158<\/h2>\n\n\n\n<p><strong>Tema 1<\/strong>. El movimiento de una part\u00edcula en el plano, se encuentra representado por las ecuaciones param\u00e9tricas:<\/p>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> x(t) = 3 \\sin ^{3}(t)-1<\/span>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> y(t) = 4 \\sin (t)\\cos (t)<\/span>\n\n\n\n<p class=\"has-text-align-center\">t\u22650<\/p>\n\n\n\n<p>Donde <strong>x<\/strong>, <strong>y<\/strong> son las coordenadas de la posici\u00f3n expresadas en <em>cm<\/em> y <strong>t<\/strong> se expresa en <em>segundos<\/em>.<\/p>\n\n\n\n<p>a) Demuestre que existe un instante <strong>t<\/strong> \u2208 [0, \u03c0\/2] tal que sus coordenadas <strong>x<\/strong> e <strong>y<\/strong> coinciden.<\/p>\n\n\n\n<p>b) Empleando el m\u00e9todo de Newton, aproxime con una precisi\u00f3n de 10<sup>-5<\/sup> en qu\u00e9 instante de tiempo las dos coordenadas ser\u00e1n iguales en el intervalo dado en el literal a.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"557\" height=\"414\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2017\/11\/s1EIIT20019T1MovPuntoPlano.png\" alt=\"intersecci\u00f3n de trayectoria de part\u00edculas en plano\" class=\"wp-image-13988\" \/><\/figure>\n\n\n\n<p><strong>Referencias<\/strong>: Megaconstrucciones, El Tren InterUrbano | M\u00e9xico - Toluca.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Megaconstrucciones, El Tren InterUrbano | M\u00e9xico - Toluca\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/i_LIJnSqYxA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>El Tunel debajo del agua entre Francia e Inglaterra<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Megaconstrucciones   El Tunel Del Canal De La Mancha\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/dhzG070kBEw?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>1ra Evaluaci\u00f3n II T\u00e9rmino 2009-2010. 1\/Diciembre\/2009. ICM00158 Tema 1. El movimiento de una part\u00edcula en el plano, se encuentra representado por las ecuaciones param\u00e9tricas: t\u22650 Donde x, y son las coordenadas de la posici\u00f3n expresadas en cm y t se expresa en segundos. a) Demuestre que existe un instante t \u2208 [0, \u03c0\/2] tal que [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-mn","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[66],"class_list":["post-439","post","type-post","status-publish","format-standard","hentry","category-mn-1eva10","tag-raices"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/439","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=439"}],"version-history":[{"count":3,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/439\/revisions"}],"predecessor-version":[{"id":13990,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/439\/revisions\/13990"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=439"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=439"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=439"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}