{"id":199310,"date":"2025-03-11T04:56:55","date_gmt":"2025-03-11T04:56:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199310"},"modified":"2025-03-11T04:56:57","modified_gmt":"2025-03-11T04:56:57","slug":"a-skier-covers-the-final-110-meters-of-a-race-in-5-0-seconds-crossing-the-finish-line-at-a-speed-of-24-m-s","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/11\/a-skier-covers-the-final-110-meters-of-a-race-in-5-0-seconds-crossing-the-finish-line-at-a-speed-of-24-m-s\/","title":{"rendered":"A skier covers the final 110 meters of a race in 5.0 seconds, crossing the finish line at a speed of 24 m\/s"},"content":{"rendered":"\n<p>A skier covers the final 110 meters of a race in 5.0 seconds, crossing the finish line at a speed of 24 m\/s. What was her (constant) acceleration?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer:<\/h3>\n\n\n\n<p>The skier&#8217;s constant acceleration is <strong>0.8 m\/s\u00b2<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To determine the acceleration of the skier, we use the kinematic equations. We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Final velocity, ( v_f = 24 ) m\/s<\/li>\n\n\n\n<li>Distance covered, ( s = 110 ) m<\/li>\n\n\n\n<li>Time taken, ( t = 5.0 ) s<\/li>\n<\/ul>\n\n\n\n<p>We assume constant acceleration and use the kinematic equations:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Equation of motion for displacement<\/strong>:<br>[<br>s = v_i t + \\frac{1}{2} a t^2<br>]<br>where ( v_i ) is the initial velocity and ( a ) is the acceleration.<\/li>\n\n\n\n<li><strong>Velocity equation<\/strong>:<br>[<br>v_f = v_i + a t<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Solve for ( v_i )<\/h3>\n\n\n\n<p>We use equation (2) to express ( v_i ):<br>[<br>v_i = v_f &#8211; a t<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Solve for ( a )<\/h3>\n\n\n\n<p>Substituting ( v_i ) in equation (1):<br>[<br>110 = (24 &#8211; a(5)) \\times 5 + \\frac{1}{2} a (5)^2<br>]<br>Expanding:<br>[<br>110 = 120 &#8211; 5a + \\frac{25}{2} a<br>]<\/p>\n\n\n\n<p>Solving for ( a ):<br>[<br>110 = 120 &#8211; 5a + 12.5a<br>]<br>[<br>110 = 120 + 7.5a<br>]<br>[<br>7.5a = -10<br>]<br>[<br>a = 0.8 \\text{ m\/s}^2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Solve for ( v_i )<\/h3>\n\n\n\n<p>[<br>v_i = 24 &#8211; (0.8 \\times 5) = 24 &#8211; 4 = 20 \\text{ m\/s}<br>]<\/p>\n\n\n\n<p>Thus, the skier\u2019s <strong>initial velocity<\/strong> was <strong>20 m\/s<\/strong>, and her <strong>constant acceleration<\/strong> was <strong>0.8 m\/s\u00b2<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-834-1024x507.png\" alt=\"\" class=\"wp-image-199311\"\/><\/figure>\n\n\n\n<p>Here is a visualization of the skier&#8217;s motion:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>first graph<\/strong> (Velocity vs. Time) shows how the skier\u2019s velocity increases linearly from <strong>20 m\/s to 24 m\/s<\/strong> over 5 seconds, confirming a constant acceleration.<\/li>\n\n\n\n<li>The <strong>second graph<\/strong> (Position vs. Time) depicts the increasing distance traveled, following a quadratic pattern due to the acceleration.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>A skier covers the final 110 meters of a race in 5.0 seconds, crossing the finish line at a speed of 24 m\/s. What was her (constant) acceleration? The correct answer and explanation is : Answer: The skier&#8217;s constant acceleration is 0.8 m\/s\u00b2. Explanation: To determine the acceleration of the skier, we use the kinematic [&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-199310","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199310","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=199310"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199310\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199310"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199310"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199310"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}