{"id":147501,"date":"2024-10-03T04:35:43","date_gmt":"2024-10-03T04:35:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=147501"},"modified":"2024-10-03T04:35:45","modified_gmt":"2024-10-03T04:35:45","slug":"a-body-with-initial-velocity-8-0-m-s-moves-along-a-straight-line-with-constant-acceleration-and-travels640-m-in-40-s","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/03\/a-body-with-initial-velocity-8-0-m-s-moves-along-a-straight-line-with-constant-acceleration-and-travels640-m-in-40-s\/","title":{"rendered":"A body with initial velocity 8.0 m\/s moves along a straight line with constant acceleration and travels640 m in 40 s"},"content":{"rendered":"\n<p>A body with initial velocity 8.0 m\/s moves along a straight line with constant acceleration and travels<br>640 m in 40 s. For the 40 s interval, find (a) the average velocity, (b) the final velocity, and (c) the<br>acceleration.\u200b<\/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\">Solution:<\/h3>\n\n\n\n<p>We are given the following information:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial velocity, ( u = 8.0 \\, \\text{m\/s} )<\/li>\n\n\n\n<li>Distance traveled, ( s = 640 \\, \\text{m} )<\/li>\n\n\n\n<li>Time interval, ( t = 40 \\, \\text{s} )<\/li>\n<\/ul>\n\n\n\n<p>Using this information, let&#8217;s solve the problem step by step.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>(a) Average velocity:<\/strong><\/p>\n\n\n\n<p>The formula for average velocity when the motion is uniformly accelerated is:<\/p>\n\n\n\n<p>[<br>v_{\\text{avg}} = \\frac{s}{t}<br>]<\/p>\n\n\n\n<p>Substituting the given values:<\/p>\n\n\n\n<p>[<br>v_{\\text{avg}} = \\frac{640 \\, \\text{m}}{40 \\, \\text{s}} = 16 \\, \\text{m\/s}<br>]<\/p>\n\n\n\n<p>So, the average velocity is ( 16 \\, \\text{m\/s} ).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>(b) Final velocity:<\/strong><\/p>\n\n\n\n<p>For uniformly accelerated motion, we can use the equation:<\/p>\n\n\n\n<p>[<br>v = u + at<br>]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( v ) is the final velocity,<\/li>\n\n\n\n<li>( a ) is the acceleration,<\/li>\n\n\n\n<li>( t ) is the time.<\/li>\n<\/ul>\n\n\n\n<p>We don&#8217;t know the acceleration yet, so first, we will use another kinematic equation to solve for ( a ):<\/p>\n\n\n\n<p>[<br>s = ut + \\frac{1}{2} a t^2<br>]<\/p>\n\n\n\n<p>Substitute the known values:<\/p>\n\n\n\n<p>[<br>640 = (8)(40) + \\frac{1}{2} a (40)^2<br>]<\/p>\n\n\n\n<p>Simplifying:<\/p>\n\n\n\n<p>[<br>640 = 320 + 800a<br>]<\/p>\n\n\n\n<p>Solving for ( a ):<\/p>\n\n\n\n<p>[<br>320 = 800a \\quad \\Rightarrow \\quad a = \\frac{320}{800} = 0.4 \\, \\text{m\/s}^2<br>]<\/p>\n\n\n\n<p>Now, substitute ( a = 0.4 \\, \\text{m\/s}^2 ) into the first equation for final velocity:<\/p>\n\n\n\n<p>[<br>v = 8 + (0.4)(40) = 8 + 16 = 24 \\, \\text{m\/s}<br>]<\/p>\n\n\n\n<p>So, the final velocity is ( 24 \\, \\text{m\/s} ).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>(c) Acceleration:<\/strong><\/p>\n\n\n\n<p>From part (b), we already found the acceleration:<\/p>\n\n\n\n<p>[<br>a = 0.4 \\, \\text{m\/s}^2<br>]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p>In kinematics, average velocity is a measure of the total displacement covered in a given time interval. For uniform acceleration, the displacement (( s )) is related to time (( t )) and initial velocity (( u )) through equations of motion. Here, we use ( v_{\\text{avg}} = \\frac{s}{t} ) to find that the object has an average velocity of 16 m\/s.<\/p>\n\n\n\n<p>Next, to calculate the final velocity (( v )), we use the second equation of motion, ( s = ut + \\frac{1}{2} at^2 ), where acceleration (( a )) is a key unknown. By substituting known values into this equation, we isolate ( a ) and determine it to be 0.4 m\/s\u00b2. This acceleration describes how much the velocity increases per second.<\/p>\n\n\n\n<p>Finally, using the equation ( v = u + at ), we find the final velocity to be 24 m\/s. The relationship between initial and final velocity is directly influenced by the acceleration, and in this case, the object gained 16 m\/s over 40 seconds due to the constant acceleration.<\/p>\n\n\n\n<p>These calculations showcase the core principles of uniformly accelerated motion, where acceleration remains constant, and both velocity and displacement follow predictable patterns over time.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A body with initial velocity 8.0 m\/s moves along a straight line with constant acceleration and travels640 m in 40 s. For the 40 s interval, find (a) the average velocity, (b) the final velocity, and (c) theacceleration.\u200b The Correct Answer and Explanation is : Solution: We are given the following information: Using this information, [&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-147501","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/147501","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=147501"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/147501\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=147501"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=147501"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=147501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}