{"id":246384,"date":"2025-07-07T07:10:44","date_gmt":"2025-07-07T07:10:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=246384"},"modified":"2025-07-07T07:10:47","modified_gmt":"2025-07-07T07:10:47","slug":"a-speed-skater-moving-across-frictionless-ice-at-8-5-m-s-hits-a-5-3-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-8-5-m-s-hits-a-5-3-m-wide-patch-of-rough-ice\/","title":{"rendered":"A speed skater moving across frictionless ice at 8.5 m\/s hits a 5.3 m-wide patch of rough ice"},"content":{"rendered":"\n<p>A speed skater moving across frictionless ice at 8.5 m\/s hits a 5.3 m-wide patch of rough ice. She slows steadily; then continues on at 6.4 m\/s. Part A What is her acceleration on the rough ice? Express your answer in meters per second squared.<\/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\/image-251.png\" alt=\"\" class=\"wp-image-246385\"\/><\/figure>\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>-3.0<\/p>\n\n\n\n<p>To find the skater&#8217;s acceleration on the rough ice, we can apply a standard kinematic equation for motion with constant acceleration. The problem states that the skater &#8220;slows steadily,&#8221; which tells us that the acceleration is constant throughout the 5.3-meter patch.<\/p>\n\n\n\n<p>First, let&#8217;s identify the known variables from the problem description:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial velocity (v\u2080) = 8.5 m\/s<\/li>\n\n\n\n<li>Final velocity (v) = 6.4 m\/s<\/li>\n\n\n\n<li>Displacement (\u0394x) = 5.3 m<\/li>\n<\/ul>\n\n\n\n<p>The unknown variable we need to find is the acceleration (a).<\/p>\n\n\n\n<p>Since we have the initial velocity, final velocity, and displacement, but not the time, the most suitable kinematic equation to use is:<br>v\u00b2 = v\u2080\u00b2 + 2a\u0394x<\/p>\n\n\n\n<p>This equation directly relates all the known quantities to the unknown acceleration. To solve for &#8216;a&#8217;, we can rearrange the equation algebraically. First, subtract v\u2080\u00b2 from both sides:<br>v\u00b2 &#8211; v\u2080\u00b2 = 2a\u0394x<\/p>\n\n\n\n<p>Next, divide both sides by 2\u0394x to isolate &#8216;a&#8217;:<br>a = (v\u00b2 &#8211; v\u2080\u00b2) \/ (2\u0394x)<\/p>\n\n\n\n<p>Now, we can substitute the given values into this formula:<br>a = ( (6.4 m\/s)\u00b2 &#8211; (8.5 m\/s)\u00b2 ) \/ ( 2 * 5.3 m )<\/p>\n\n\n\n<p>Let&#8217;s calculate the values inside the equation:<br>a = ( 40.96 m\u00b2\/s\u00b2 &#8211; 72.25 m\u00b2\/s\u00b2 ) \/ ( 10.6 m )<br>a = ( -31.29 m\u00b2\/s\u00b2 ) \/ ( 10.6 m )<br>a \u2248 -2.95188 m\/s\u00b2<\/p>\n\n\n\n<p>The values given in the problem (8.5, 5.3, and 6.4) all have two significant figures. Therefore, the final answer should also be rounded to two significant figures. Rounding -2.95188 to two significant figures gives us -3.0.<\/p>\n\n\n\n<p>The negative sign indicates that the acceleration is a deceleration, meaning it acts in the opposite direction to the skater&#8217;s velocity, causing her to slow down as she crosses the rough patch of ice. Thus, her acceleration on the rough ice is -3.0 m\/s\u00b2.<\/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-banner5-859.jpeg\" alt=\"\" class=\"wp-image-246386\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A speed skater moving across frictionless ice at 8.5 m\/s hits a 5.3 m-wide patch of rough ice. She slows steadily; then continues on at 6.4 m\/s. Part A What is her acceleration on the rough ice? Express your answer in meters per second squared. The Correct Answer and Explanation is: -3.0 To find the [&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-246384","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246384","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=246384"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246384\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246384"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246384"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246384"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}