{"id":246389,"date":"2025-07-07T07:12:30","date_gmt":"2025-07-07T07:12:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=246389"},"modified":"2025-07-07T07:12:32","modified_gmt":"2025-07-07T07:12:32","slug":"a-speed-skater-moving-across-frictionless-ice-at-9-0-m-s-hits-a-5-0-m-wide-patch-of-rough-ice","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/07\/a-speed-skater-moving-across-frictionless-ice-at-9-0-m-s-hits-a-5-0-m-wide-patch-of-rough-ice\/","title":{"rendered":"A speed skater moving across frictionless ice at 9.0 m\/s hits a 5.0 m -wide patch of rough ice."},"content":{"rendered":"\n<p>A speed skater moving across frictionless ice at 9.0 m\/s hits a 5.0 m -wide patch of rough ice. She slows steadily, then continues on at 6.5 m\/s . What is her acceleration on the rough ice?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine the skater&#8217;s acceleration on the rough ice, we can use the following kinematic equation:vf2=vi2+2adv_f^2 = v_i^2 + 2a dvf2\u200b=vi2\u200b+2ad<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>vfv_fvf\u200b is the final velocity (6.5 m\/s)<\/li>\n\n\n\n<li>viv_ivi\u200b is the initial velocity (9.0 m\/s)<\/li>\n\n\n\n<li>aaa is the acceleration (what we want to find)<\/li>\n\n\n\n<li>ddd is the distance traveled over the rough ice (5.0 m)<\/li>\n<\/ul>\n\n\n\n<p>We can rearrange the equation to solve for acceleration:a=vf2\u2212vi22da = \\frac{v_f^2 &#8211; v_i^2}{2d}a=2dvf2\u200b\u2212vi2\u200b\u200b<\/p>\n\n\n\n<p>Substituting the known values:a=(6.5)2\u2212(9.0)22(5.0)a = \\frac{(6.5)^2 &#8211; (9.0)^2}{2(5.0)}a=2(5.0)(6.5)2\u2212(9.0)2\u200ba=42.25\u221281.010a = \\frac{42.25 &#8211; 81.0}{10}a=1042.25\u221281.0\u200ba=\u221238.7510a = \\frac{-38.75}{10}a=10\u221238.75\u200ba=\u22123.875\u2009m\/s2a = -3.875 \\, \\text{m\/s}^2a=\u22123.875m\/s2<\/p>\n\n\n\n<p>So, the skater&#8217;s acceleration on the rough ice is \u22123.875\u2009m\/s2-3.875 \\, \\text{m\/s}^2\u22123.875m\/s2. The negative sign indicates that the skater is slowing down (decelerating).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The equation used is a fundamental equation of motion that describes how velocity changes with constant acceleration over a certain distance. In this case, the skater starts with an initial velocity of 9.0 m\/s, moves across the rough patch of ice (which slows her down), and finishes with a final velocity of 6.5 m\/s. Since she is slowing down, the acceleration is negative, indicating a decrease in speed. The magnitude of the acceleration, 3.875 m\/s\u00b2, tells us how much her speed decreases for each second she is on the rough ice.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-860.jpeg\" alt=\"\" class=\"wp-image-246390\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A speed skater moving across frictionless ice at 9.0 m\/s hits a 5.0 m -wide patch of rough ice. She slows steadily, then continues on at 6.5 m\/s . What is her acceleration on the rough ice? The Correct Answer and Explanation is: To determine the skater&#8217;s acceleration on the rough ice, we can use [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-246389","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=246389"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246389\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}