A car starts from rest and accelerates at a constant 1.5 m\/s2. Some time later, it takes 2.1 s to cross over a 25-meter long bridge. How far did the car travel before getting onto the bridge?<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n The car traveled approximately 35.57 meters<\/strong> before reaching the bridge.<\/p>\n\n\n\n The problem involves kinematics with constant acceleration<\/strong>. The car starts from rest, meaning its initial velocity (uu) is 0<\/strong>. It accelerates at 1.5 m\/s\u00b2<\/strong> until it reaches the bridge.<\/p>\n\n\n\n While crossing the 25-meter<\/strong> bridge in 2.1 seconds<\/strong>, we use the kinematic equation: d=vinitial\u22c5t+12at2d = v_{\\text{initial}} \\cdot t + \\frac{1}{2} a t^2<\/p>\n\n\n\n Plugging in the given values: 25=vinitial\u22c5(2.1)+12(1.5)(2.1)225 = v_{\\text{initial}} \\cdot (2.1) + \\frac{1}{2} (1.5) (2.1)^2<\/p>\n\n\n\n Solving for vinitialv_{\\text{initial}}, we get: vinitial=9.82 m\/sv_{\\text{initial}} = 9.82 \\text{ m\/s}<\/p>\n\n\n\n This is the velocity just before<\/strong> reaching the bridge.<\/p>\n\n\n\n Using the formula: v=u+atv = u + at<\/p>\n\n\n\n Since the car starts from rest (u=0u = 0): 9.82=(1.5)t9.82 = (1.5) t<\/p>\n\n\n\n Solving for tt, we get: t=6.55 secondst = 6.55 \\text{ seconds}<\/p>\n\n\n\n So, it took 6.55 seconds<\/strong> to reach the bridge.<\/p>\n\n\n\n Using: d=ut+12at2d = ut + \\frac{1}{2} a t^2 d=0+12(1.5)(6.55)2d = 0 + \\frac{1}{2} (1.5) (6.55)^2 d=35.57 metersd = 35.57 \\text{ meters}<\/p>\n\n\n\n Thus, the car traveled 35.57 meters<\/strong> before reaching the bridge.<\/p>\n","protected":false},"excerpt":{"rendered":" A car starts from rest and accelerates at a constant 1.5 m\/s2. Some time later, it takes 2.1 s to cross over a 25-meter long bridge. How far did the car travel before getting onto the bridge? The correct answer and explanation is : The car traveled approximately 35.57 meters before reaching the bridge. Explanation: […]<\/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-199305","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199305","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=199305"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199305\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199305"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199305"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199305"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
Step 1: Find the velocity at the moment the car reaches the bridge<\/strong><\/h4>\n\n\n\n
Step 2: Determine the time taken to reach the bridge<\/strong><\/h4>\n\n\n\n
Step 3: Calculate the distance before the bridge<\/strong><\/h4>\n\n\n\n