{"id":6552,"date":"2011-03-01T17:31:35","date_gmt":"2011-03-01T17:31:35","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6552"},"modified":"2022-01-23T15:58:06","modified_gmt":"2022-01-23T15:58:06","slug":"um-atleta-percorre-uma-pista-de-100-metros","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6552","title":{"rendered":"Um atleta percorre uma pista de 100 metros"},"content":{"rendered":"<p><ul id='GTTabs_ul_6552' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6552' class='GTTabs_curr'><a  id=\"6552_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6552' ><a  id=\"6552_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6552'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um atleta percorre uma pista de 100 metros de modo a que a dist\u00e2ncia d(t), em metros, percorrida ap\u00f3s t segundos, \u00e9 dada por:<br \/>\n\\[d(t)=0,2{{t}^{2}}+8t\\]<\/p>\n<p>Determine o valor da velocidade do atleta:<\/p>\n<ol>\n<li>no in\u00edcio da corrida;<\/li>\n<li>quando $t=10$ s;<\/li>\n<li>ao chegar \u00e0 meta.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6552' onClick='GTTabs_show(1,6552)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6552'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>A velocidade do atleta \u00e9 dada por $d&#8217;(t)=0,4t+8$.\n<p>Logo, no in\u00edcio da corrida a sua velocidade \u00e9 $d&#8217;(0)=0,4\\times 0+8=8\\,m\/s$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>Quando $t=10$ s, a sua velocidade \u00e9 $d&#8217;(10)=0,4\\times 10+8=12\\,m\/s$.<br \/>\n\u00ad<\/li>\n<li>Ora, \\[\\begin{array}{*{35}{l}}<br \/>\nd(t)=100 &amp; \\Leftrightarrow\u00a0 &amp; 0,2{{t}^{2}}+8t=100\\wedge t\\ge 0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; t=\\frac{-8\\pm \\sqrt{64+80}}{0,4}\\wedge t\\ge 0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; (t=-50\\vee t=10)\\wedge t\\ge 0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; t=10\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>O atleta chega \u00e0 meta, 10 segundos ap\u00f3s a partida, com uma velocidade de $d&#8217;(10)=0,4\\times 10+8=12\\,m\/s$.<\/p>\n<p style=\"text-align: center;\" data-tadv-p=\"keep\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6553\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6553\" 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srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-1.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-1-150x77.jpg 150w\" sizes=\"auto, (max-width: 211px) 100vw, 211px\" \/><\/a>\u00a0 <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6554\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6554\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-2.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-2.jpg\" class=\"alignnone size-full wp-image-6554\" title=\"G1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-2.jpg\" alt=\"\" width=\"211\" height=\"109\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-2.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-2-150x77.jpg 150w\" sizes=\"auto, (max-width: 211px) 100vw, 211px\" \/><\/a>\u00a0 <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6555\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6555\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-3.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-3.jpg\" class=\"alignnone size-full wp-image-6555\" title=\"G2\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-3.jpg\" alt=\"\" width=\"211\" height=\"109\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-3.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-193-34-3-150x77.jpg 150w\" sizes=\"auto, (max-width: 211px) 100vw, 211px\" \/><\/a><\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6552' onClick='GTTabs_show(0,6552)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um atleta percorre uma pista de 100 metros de modo a que a dist\u00e2ncia d(t), em metros, percorrida ap\u00f3s t segundos, \u00e9 dada por: \\[d(t)=0,2{{t}^{2}}+8t\\] Determine o valor da velocidade do&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20917,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,134],"tags":[136],"series":[],"class_list":["post-6552","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-derivadas","tag-derivada"],"views":3988,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11V2Pag193-34_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6552","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6552"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6552\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20917"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6552"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6552"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6552"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}