{"id":199562,"date":"2025-03-12T06:12:53","date_gmt":"2025-03-12T06:12:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199562"},"modified":"2025-03-12T06:12:55","modified_gmt":"2025-03-12T06:12:55","slug":"a-police-officer-is-called-in-for-accident-reconstruction-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/12\/a-police-officer-is-called-in-for-accident-reconstruction-3\/","title":{"rendered":"A police officer is called in for accident reconstruction"},"content":{"rendered":"\n

A police officer is called in for accident reconstruction. He measures 11-meter long skid marks and he knows that for that particular tire\/pavement combination, the coefficient of kinetic friction is 0.65. He also knows that the car was traveling at 3.5 m\/s just before impact (the end of the skid marks). What was the speed of the car before it began the skid? Convert this to miles per hour. (Note: 1 mile = 1609 meters).<\/p>\n\n\n\n

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

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

The speed of the car before it began skidding was 12.35 m\/s<\/strong>, which converts to 27.63 mph<\/strong>.<\/p>\n\n\n\n

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

When a vehicle leaves skid marks, the length of the marks can be used to determine the vehicle’s speed before braking. We use the kinematic equation:<\/p>\n\n\n\n

[
v^2 = u^2 + 2as
]<\/p>\n\n\n\n

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

    \n
  • ( v ) = final speed (3.5 m\/s, just before impact),<\/li>\n\n\n\n
  • ( u ) = initial speed before skidding (to be determined),<\/li>\n\n\n\n
  • ( a ) = acceleration due to friction, which is negative because it slows the vehicle down,<\/li>\n\n\n\n
  • ( s ) = skid distance (11 meters),<\/li>\n\n\n\n
  • ( a = – (\\mu g) ), where ( \\mu = 0.65 ) (coefficient of kinetic friction) and ( g = 9.81 ) m\/s\u00b2 (acceleration due to gravity).<\/li>\n<\/ul>\n\n\n\n

    Step 1: Compute acceleration<\/h4>\n\n\n\n

    [
    a = – (0.65 \\times 9.81) = -6.3765 \\text{ m\/s}^2
    ]<\/p>\n\n\n\n

    Step 2: Solve for ( u )<\/h4>\n\n\n\n

    [
    u = \\sqrt{v^2 – 2as}
    ]<\/p>\n\n\n\n

    [
    u = \\sqrt{(3.5)^2 – 2(-6.3765)(11)}
    ]<\/p>\n\n\n\n

    [
    u = \\sqrt{12.25 + 140.283}
    ]<\/p>\n\n\n\n

    [
    u = \\sqrt{152.533} \\approx 12.35 \\text{ m\/s}
    ]<\/p>\n\n\n\n

    Step 3: Convert to mph<\/h4>\n\n\n\n

    [
    u_{\\text{mph}} = \\frac{12.35 \\times 3600}{1609} \\approx 27.63 \\text{ mph}
    ]<\/p>\n\n\n\n

    This means that before the driver started skidding, the car was traveling at approximately 27.63 miles per hour<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    A police officer is called in for accident reconstruction. He measures 11-meter long skid marks and he knows that for that particular tire\/pavement combination, the coefficient of kinetic friction is 0.65. He also knows that the car was traveling at 3.5 m\/s just before impact (the end of the skid marks). What was the speed […]<\/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-199562","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199562","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=199562"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199562\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199562"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199562"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199562"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}