{"id":406,"date":"2023-06-19T08:23:26","date_gmt":"2023-06-19T08:23:26","guid":{"rendered":"https:\/\/physigeek.com\/pt\/aceleracao-instantanea\/"},"modified":"2023-06-19T08:23:26","modified_gmt":"2023-06-19T08:23:26","slug":"aceleracao-instantanea","status":"publish","type":"post","link":"https:\/\/physigeek.com\/pt\/aceleracao-instantanea\/","title":{"rendered":"Acelera\u00e7\u00e3o instant\u00e2nea"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 acelera\u00e7\u00e3o instant\u00e2nea na f\u00edsica. Da mesma forma, voc\u00ea descobrir\u00e1 como calcular a acelera\u00e7\u00e3o instant\u00e2nea e, al\u00e9m disso, um exerc\u00edcio resolvido sobre acelera\u00e7\u00e3o instant\u00e2nea. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-la-aceleracion-instantanea\"><\/span> O que \u00e9 acelera\u00e7\u00e3o instant\u00e2nea?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A acelera\u00e7\u00e3o instant\u00e2nea<\/strong> \u00e9 a acelera\u00e7\u00e3o que um corpo tem em um instante espec\u00edfico. Em outras palavras, a acelera\u00e7\u00e3o instant\u00e2nea de um corpo num determinado instante \u00e9 a acelera\u00e7\u00e3o que ele possui naquele momento.<\/p>\n<p> Portanto, a acelera\u00e7\u00e3o instant\u00e2nea de um corpo pode mudar a cada instante do andamento. Assim, um corpo em movimento pode ter uma acelera\u00e7\u00e3o instant\u00e2nea diferente a cada instante.<\/p>\n<p> Por exemplo, se a acelera\u00e7\u00e3o instant\u00e2nea de um m\u00f3vel no instante t=7 s for igual a 3 m\/s <sup>2<\/sup> , isso significa que o corpo est\u00e1 se movendo com uma acelera\u00e7\u00e3o de 3 m\/s <sup>2<\/sup> no instante t=7 s. Portanto, como a acelera\u00e7\u00e3o instant\u00e2nea \u00e9 positiva, a velocidade do corpo ser\u00e1 maior ap\u00f3s esse instante.<\/p>\n<p> Uma das caracter\u00edsticas da acelera\u00e7\u00e3o instant\u00e2nea \u00e9 que sua dire\u00e7\u00e3o e sentido podem ser diferentes do movimento. Por exemplo, a velocidade instant\u00e2nea de um trem em frenagem avan\u00e7a (ele continua a avan\u00e7ar), mas o vetor de acelera\u00e7\u00e3o instant\u00e2nea retrocede porque a velocidade diminui. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-la-aceleracion-instantanea\"><\/span> F\u00f3rmula de acelera\u00e7\u00e3o instant\u00e2nea<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Matematicamente, a acelera\u00e7\u00e3o instant\u00e2nea \u00e9 definida como o limite da acelera\u00e7\u00e3o m\u00e9dia conforme o intervalo de tempo se aproxima de zero. Portanto, a acelera\u00e7\u00e3o instant\u00e2nea \u00e9 igual \u00e0 derivada do vetor velocidade instant\u00e2nea em rela\u00e7\u00e3o ao tempo.<\/p>\n<p> Portanto, a <strong>f\u00f3rmula da acelera\u00e7\u00e3o instant\u00e2nea<\/strong> \u00e9:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-2ddee6150f0228c035c4acb4ffb4a148_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\vv{a_i}=\\lim_{\\Delta t\\to 0}\\vv{a_m}=\\lim_{\\Delta t\\to 0}\\frac{\\Delta \\vv{v_i}}{\\ Delta t}=\\frac{d\\vv{v_i}}{dt}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"275\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-14cb9e3125e02a9b4aca54a32463b5e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"14\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o vetor de acelera\u00e7\u00e3o instant\u00e2nea. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e2c27fee8a0bbbaa20c127a1bedbcd9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a_m}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"21\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o vetor de acelera\u00e7\u00e3o m\u00e9dia. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-444fb95ef6e118a991b45d7099a7a5e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta \\vv{v_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"29\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o vetor velocidade instant\u00e2nea. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-819ab50990df5adf82bea9dfa75ffff2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta t\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o intervalo de tempo que tende a 0, ou seja, um intervalo de tempo infinitamente pequeno. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-9236b0ddce5ddfd56928e080c80c5260_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{d\\vv{v_i}}{dt}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"24\" style=\"vertical-align: -12px;\"><\/p>\n<p> \u00e9 a derivada do vetor velocidade instant\u00e2nea em rela\u00e7\u00e3o ao tempo.<\/span><\/li>\n<\/ul>\n<p> Tenha em mente que a velocidade instant\u00e2nea \u00e9 a derivada do vetor posi\u00e7\u00e3o em rela\u00e7\u00e3o ao tempo. Voc\u00ea pode ver como \u00e9 calculado clicando aqui: <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/physigeek.com\/pt\">Como calcular a velocidade instant\u00e2nea<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-resuelto-de-la-aceleracion-instantanea\"><\/span> Exemplo concreto de acelera\u00e7\u00e3o instant\u00e2nea<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que sabemos a defini\u00e7\u00e3o de acelera\u00e7\u00e3o instant\u00e2nea e qual \u00e9 sua f\u00f3rmula, nesta se\u00e7\u00e3o voc\u00ea poder\u00e1 ver um exemplo concreto de como a acelera\u00e7\u00e3o instant\u00e2nea \u00e9 calculada.<\/p>\n<ul>\n<li> O vetor posi\u00e7\u00e3o de um corpo \u00e9 definido em fun\u00e7\u00e3o do tempo pela seguinte equa\u00e7\u00e3o:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-4436612845651cdfe74563983a1993bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r}(t)=t^3-4t^2-5t+9\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"179\" style=\"vertical-align: -5px;\"><\/p>\n<p> . Qual \u00e9 a acelera\u00e7\u00e3o instant\u00e2nea do corpo no instante t=2s?<\/li>\n<\/ul>\n<p> Para encontrar a equa\u00e7\u00e3o da acelera\u00e7\u00e3o instant\u00e2nea, devemos primeiro encontrar a equa\u00e7\u00e3o da velocidade instant\u00e2nea. Para fazer isso, derivamos a equa\u00e7\u00e3o de posi\u00e7\u00e3o em rela\u00e7\u00e3o ao tempo:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-4436612845651cdfe74563983a1993bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r}(t)=t^3-4t^2-5t+9\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"179\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-76b94cd03386a16c96a69f801494d3e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{v_i}(t)=\\cfrac{d\\vv{r}}{dt}=3t^2-8t-5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"191\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ent\u00e3o diferenciamos novamente em rela\u00e7\u00e3o ao tempo para obter a equa\u00e7\u00e3o da acelera\u00e7\u00e3o instant\u00e2nea:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-b052662130ceb833e6435db7dfe27876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a_i}(t)=\\cfrac{d\\vv{v_i}}{dt}=6t-8\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"154\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Uma vez calculada a express\u00e3o para a acelera\u00e7\u00e3o instant\u00e2nea, basta substituir o instante t=2s na equa\u00e7\u00e3o e resolver os c\u00e1lculos: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-1321d46d8bd02e98330c9aaccf45dfce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{a_i}(2)=6\\cdot 2-8=4 \\ \\cfrac{m}{s^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"180\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Aceleracion-instantanea-y-aceleracion-media\"><\/span> Acelera\u00e7\u00e3o instant\u00e2nea e acelera\u00e7\u00e3o m\u00e9dia<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Por fim, veremos qual a diferen\u00e7a entre acelera\u00e7\u00e3o instant\u00e2nea e acelera\u00e7\u00e3o m\u00e9dia, pois s\u00e3o dois tipos de acelera\u00e7\u00e3o que devem ser diferenciados na cinem\u00e1tica.<\/p>\n<p> A <strong>acelera\u00e7\u00e3o m\u00e9dia<\/strong> \u00e9 a acelera\u00e7\u00e3o na qual um corpo em movimento teria viajado se tivesse se movido com uma acelera\u00e7\u00e3o constante ao longo do caminho.<\/p>\n<p> A <strong>diferen\u00e7a entre acelera\u00e7\u00e3o instant\u00e2nea e acelera\u00e7\u00e3o m\u00e9dia<\/strong> \u00e9 que acelera\u00e7\u00e3o instant\u00e2nea \u00e9 a acelera\u00e7\u00e3o que um corpo tem em um determinado instante, enquanto acelera\u00e7\u00e3o m\u00e9dia \u00e9 a acelera\u00e7\u00e3o que um corpo teria se estivesse se movendo com acelera\u00e7\u00e3o constante.<\/p>\n<p> Deve-se notar que a acelera\u00e7\u00e3o instant\u00e2nea tamb\u00e9m pode ser definida como a acelera\u00e7\u00e3o m\u00e9dia de um intervalo de tempo muito pequeno, t\u00e3o pequeno que \u00e9 considerado um \u00fanico instante de tempo. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/physigeek.com\/pt\/aceleracao-media\/\">O que \u00e9 acelera\u00e7\u00e3o m\u00e9dia?<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 acelera\u00e7\u00e3o instant\u00e2nea na f\u00edsica. Da mesma forma, voc\u00ea descobrir\u00e1 como calcular a acelera\u00e7\u00e3o instant\u00e2nea e, al\u00e9m disso, um exerc\u00edcio resolvido sobre acelera\u00e7\u00e3o instant\u00e2nea. O que \u00e9 acelera\u00e7\u00e3o instant\u00e2nea? A acelera\u00e7\u00e3o instant\u00e2nea \u00e9 a acelera\u00e7\u00e3o que um corpo tem em um instante espec\u00edfico. Em outras palavras, a acelera\u00e7\u00e3o instant\u00e2nea de &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/pt\/aceleracao-instantanea\/\"> <span class=\"screen-reader-text\">Acelera\u00e7\u00e3o instant\u00e2nea<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-406","post","type-post","status-publish","format-standard","hentry","category-cinematografico"],"yoast_head":"<!-- This site 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