{"id":228334,"date":"2025-06-07T08:12:25","date_gmt":"2025-06-07T08:12:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228334"},"modified":"2025-06-07T08:12:28","modified_gmt":"2025-06-07T08:12:28","slug":"using-mrua-formulas-uniformly-accelerated-rectilinear-motion-find-the-speed-that-a-body-acquires-that-has-an-initial-speed-of-35-m-s-and-decelerates-at-a-rate-of-7-m-s2-that-is-its-speed-decreas","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/using-mrua-formulas-uniformly-accelerated-rectilinear-motion-find-the-speed-that-a-body-acquires-that-has-an-initial-speed-of-35-m-s-and-decelerates-at-a-rate-of-7-m-s2-that-is-its-speed-decreas\/","title":{"rendered":"Using MRUA formulas (Uniformly Accelerated Rectilinear Motion), find the speed that a body acquires that has an initial speed of 35 m\/s and decelerates at a rate of 7 m\/s^2 (that is, its speed decreases at a rate of 7 m\/s for every second that passes)"},"content":{"rendered":"\n

Using MRUA formulas (Uniformly Accelerated Rectilinear Motion), find the speed that a body acquires that has an initial speed of 35 m\/s and decelerates at a rate of 7 m\/s^2 (that is, its speed decreases at a rate of 7 m\/s for every second that passes). What is the time that passes for the body to come to a complete stop, that is, when its final speed is ZERO<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To solve this problem, we use the Uniformly Accelerated Rectilinear Motion (MRUA)<\/strong> formulas. The situation describes a body decelerating<\/strong> (slowing down) from an initial speed of 35 m\/s at a constant rate of 7 m\/s\u00b2 until it comes to a complete stop<\/strong> (final speed is 0 m\/s).<\/p>\n\n\n\n

\n\n\n\n

1. Given:<\/strong><\/h3>\n\n\n\n
    \n
  • Initial speed v0=35\u2009m\/sv_0 = 35 \\, \\text{m\/s}v0\u200b=35m\/s<\/li>\n\n\n\n
  • Final speed v=0\u2009m\/sv = 0 \\, \\text{m\/s}v=0m\/s<\/li>\n\n\n\n
  • Acceleration a=\u22127\u2009m\/s2a = -7 \\, \\text{m\/s}^2a=\u22127m\/s2 (negative because it is deceleration)<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    2. Formula to Use:<\/strong><\/h3>\n\n\n\n

    We use the MRUA formula: v=v0+atv = v_0 + a tv=v0\u200b+at<\/p>\n\n\n\n

    We need to find the time ttt when the final speed v=0v = 0v=0.<\/p>\n\n\n\n

    Substitute the known values: 0=35+(\u22127)t0 = 35 + (-7)t0=35+(\u22127)t 0=35\u22127t0 = 35 – 7t0=35\u22127t 7t=357t = 357t=35 t=357=5\u2009secondst = \\frac{35}{7} = 5 \\, \\text{seconds}t=735\u200b=5seconds<\/p>\n\n\n\n

    \n\n\n\n

    Answer:<\/strong><\/h3>\n\n\n\n
      \n
    • The body takes 5 seconds<\/strong> to come to a complete stop.<\/li>\n\n\n\n
    • At that point, its final speed is 0 m\/s<\/strong> (as given).<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

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

      In physics, uniformly accelerated rectilinear motion (MRUA) describes motion in a straight line where the acceleration is constant. When a body decelerates, it experiences a negative acceleration. This means that with every second that passes, the speed of the object decreases by a fixed amount.<\/p>\n\n\n\n

      In this problem, the body starts with an initial speed of 35 meters per second and decelerates at a rate of 7 meters per second squared. Since deceleration means the speed reduces steadily, the object’s speed reduces by 7 m\/s every second.<\/p>\n\n\n\n

      To find how long it takes for the object to come to a complete stop (where the final speed is 0), we use the MRUA formula: v=v0+atv = v_0 + a tv=v0\u200b+at<\/p>\n\n\n\n

      Where:<\/p>\n\n\n\n

        \n
      • vvv is the final velocity,<\/li>\n\n\n\n
      • v0v_0v0\u200b is the initial velocity,<\/li>\n\n\n\n
      • aaa is the acceleration,<\/li>\n\n\n\n
      • ttt is the time.<\/li>\n<\/ul>\n\n\n\n

        Plugging in the values: 0=35\u22127t0 = 35 – 7t0=35\u22127t. Solving this, we find that t=5t = 5t=5 seconds. This tells us that the body will continue to slow down for 5 seconds before it fully stops.<\/p>\n\n\n\n

        This makes sense because, with a deceleration of 7 m\/s\u00b2, each second reduces the speed by 7 m\/s. In five seconds, the speed reduces by 5\u00d77=35\u2009m\/s5 \\times 7 = 35 \\, \\text{m\/s}5\u00d77=35m\/s, which exactly cancels out the initial speed of 35 m\/s, leaving the object at rest.<\/p>\n\n\n\n

        This analysis is a practical example of MRUA, demonstrating how time and acceleration relate to changes in velocity.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Using MRUA formulas (Uniformly Accelerated Rectilinear Motion), find the speed that a body acquires that has an initial speed of 35 m\/s and decelerates at a rate of 7 m\/s^2 (that is, its speed decreases at a rate of 7 m\/s for every second that passes). What is the time that passes for the body […]<\/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-228334","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228334","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=228334"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228334\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228334"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228334"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228334"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}