{"id":199547,"date":"2025-03-12T05:33:39","date_gmt":"2025-03-12T05:33:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199547"},"modified":"2025-03-12T05:33:41","modified_gmt":"2025-03-12T05:33:41","slug":"a-skier-covers-the-final-110-meters-of-a-race-in-5-0-seconds","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/12\/a-skier-covers-the-final-110-meters-of-a-race-in-5-0-seconds\/","title":{"rendered":"A skier covers the final 110 meters of a race in 5.0 seconds"},"content":{"rendered":"\n

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

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

The skier’s constant acceleration is 0.80 m\/s\u00b2<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

We are given:<\/p>\n\n\n\n

    \n
  • The final distance covered: 110 m<\/strong><\/li>\n\n\n\n
  • The time taken: 5.0 s<\/strong><\/li>\n\n\n\n
  • The final velocity: 24 m\/s<\/strong><\/li>\n<\/ul>\n\n\n\n

    To find the constant acceleration<\/strong>, we use kinematic equations<\/strong>.<\/p>\n\n\n\n

    Step 1: Use the kinematic equation for displacement:<\/h4>\n\n\n\n

    [
    d = v_i t + \\frac{1}{2} a t^2
    ]
    where:<\/p>\n\n\n\n

      \n
    • ( d = 110 ) m,<\/li>\n\n\n\n
    • ( t = 5.0 ) s,<\/li>\n\n\n\n
    • ( v_i ) is the initial velocity,<\/li>\n\n\n\n
    • ( a ) is the acceleration.<\/li>\n<\/ul>\n\n\n\n

      Step 2: Use the velocity equation:<\/h4>\n\n\n\n

      [
      v_f = v_i + a t
      ]
      where:<\/p>\n\n\n\n

        \n
      • ( v_f = 24 ) m\/s.<\/li>\n<\/ul>\n\n\n\n

        Step 3: Solve for ( v_i ) and ( a )<\/h4>\n\n\n\n

        We solve these two equations simultaneously:<\/p>\n\n\n\n

          \n
        1. ( 110 = v_i (5) + \\frac{1}{2} a (5^2) ) \u2192 ( 110 = 5v_i + 12.5a )<\/li>\n\n\n\n
        2. ( 24 = v_i + 5a )<\/li>\n<\/ol>\n\n\n\n

          Solving these equations:<\/p>\n\n\n\n

            \n
          • ( v_i = 20 ) m\/s (initial velocity)<\/li>\n\n\n\n
          • ( a = 0.80 ) m\/s\u00b2 (acceleration)<\/li>\n<\/ul>\n\n\n\n

            Thus, the skier’s acceleration is 0.80 m\/s\u00b2<\/strong>.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            The plots above illustrate the skier’s motion:<\/p>\n\n\n\n

              \n
            1. Velocity vs. Time<\/strong> (Left Graph) – The skier’s velocity increases linearly over time due to the constant acceleration of 0.80 m\/s\u00b2<\/strong>.<\/li>\n\n\n\n
            2. Position vs. Time<\/strong> (Right Graph) – The distance covered follows a quadratic trend, as the skier’s speed increases over time.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"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. What was her (constant) acceleration? The correct answer and explanation is : The skier’s constant acceleration is 0.80 m\/s\u00b2. Explanation: We are given: To find the constant acceleration, we use kinematic equations. […]<\/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-199547","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199547","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=199547"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199547\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199547"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199547"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199547"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}