{"id":188153,"date":"2025-02-06T12:19:30","date_gmt":"2025-02-06T12:19:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188153"},"modified":"2025-02-06T12:19:32","modified_gmt":"2025-02-06T12:19:32","slug":"a-car-starts-from-rest-and-travels-along-a-straight-track-such-that-it-accelerates-at-8-m-s2for-10-s-and-then-decelerates-at-1-27-m-s2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/06\/a-car-starts-from-rest-and-travels-along-a-straight-track-such-that-it-accelerates-at-8-m-s2for-10-s-and-then-decelerates-at-1-27-m-s2\/","title":{"rendered":"A car starts from rest and travels along a straight track such that it accelerates at 8 m\/s2for 10 s and then decelerates at 1.27 m\/s2"},"content":{"rendered":"\n

A car starts from rest and travels along a straight track such that it accelerates at 8 m\/s2for 10 s and then decelerates at 1.27 m\/s2. Determine the distance (in m) travelled by the car in + = 25 seconds. Round off only on the final answer expressed in three decimal places.<\/p>\n\n\n\n

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

To determine the total distance traveled by the car, we need to break the problem into two parts: the acceleration phase and the deceleration phase.<\/p>\n\n\n\n

Given Data:<\/h3>\n\n\n\n
    \n
  1. The car starts from rest, so the initial velocity ( u = 0 \\, \\text{m\/s} ).<\/li>\n\n\n\n
  2. Acceleration during the first phase ( a_1 = 8 \\, \\text{m\/s}^2 ), and the time for this phase is ( t_1 = 10 \\, \\text{s} ).<\/li>\n\n\n\n
  3. Deceleration during the second phase ( a_2 = -1.27 \\, \\text{m\/s}^2 ), and the total time is ( t_2 = 25 – 10 = 15 \\, \\text{s} ).<\/li>\n<\/ol>\n\n\n\n

    Step 1: Distance traveled during acceleration phase (first 10 seconds)<\/h3>\n\n\n\n

    For the first 10 seconds, the car accelerates at ( 8 \\, \\text{m\/s}^2 ), starting from rest. We can use the following kinematic equation to calculate the distance traveled:<\/p>\n\n\n\n

    [
    d_1 = u t + \\frac{1}{2} a t^2
    ]<\/p>\n\n\n\n

    Substitute the values:<\/p>\n\n\n\n

    [
    d_1 = 0 \\times 10 + \\frac{1}{2} \\times 8 \\times (10)^2 = 4 \\times 100 = 400 \\, \\text{m}
    ]<\/p>\n\n\n\n

    Step 2: Velocity at the end of acceleration phase<\/h3>\n\n\n\n

    At the end of the 10 seconds, the velocity of the car will be:<\/p>\n\n\n\n

    [
    v_1 = u + a_1 t_1 = 0 + 8 \\times 10 = 80 \\, \\text{m\/s}
    ]<\/p>\n\n\n\n

    Step 3: Distance traveled during deceleration phase (next 15 seconds)<\/h3>\n\n\n\n

    During the deceleration phase, the car slows down at ( 1.27 \\, \\text{m\/s}^2 ) for 15 seconds. The initial velocity at the beginning of this phase is ( v_1 = 80 \\, \\text{m\/s} ). To calculate the distance traveled during deceleration, we use the same kinematic equation:<\/p>\n\n\n\n

    [
    d_2 = v_1 t_2 + \\frac{1}{2} a_2 t_2^2
    ]<\/p>\n\n\n\n

    Substitute the values:<\/p>\n\n\n\n

    [
    d_2 = 80 \\times 15 + \\frac{1}{2} \\times (-1.27) \\times (15)^2
    ]
    [
    d_2 = 1200 + \\frac{1}{2} \\times (-1.27) \\times 225
    ]
    [
    d_2 = 1200 – 142.875 = 1057.125 \\, \\text{m}
    ]<\/p>\n\n\n\n

    Step 4: Total distance traveled<\/h3>\n\n\n\n

    The total distance traveled is the sum of the distances during both phases:<\/p>\n\n\n\n

    [
    d_{\\text{total}} = d_1 + d_2 = 400 + 1057.125 = 1457.125 \\, \\text{m}
    ]<\/p>\n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    The total distance traveled by the car is 1457.125 meters<\/strong>.<\/p>\n\n\n\n

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

    A car starts from rest and travels along a straight track such that it accelerates at 8 m\/s2for 10 s and then decelerates at 1.27 m\/s2. Determine the distance (in m) travelled by the car in + = 25 seconds. Round off only on the final answer expressed in three decimal places. The Correct Answer […]<\/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-188153","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188153","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=188153"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188153\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}