{"id":181405,"date":"2025-01-10T17:53:40","date_gmt":"2025-01-10T17:53:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=181405"},"modified":"2025-01-10T17:53:43","modified_gmt":"2025-01-10T17:53:43","slug":"b-at-time-t-3-is-chloes-speed-increasing-or-decreasing","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/10\/b-at-time-t-3-is-chloes-speed-increasing-or-decreasing\/","title":{"rendered":"b) At time t = 3, is Chloe’s speed increasing or decreasing"},"content":{"rendered":"\n

b) At time t = 3, is Chloe’s speed increasing or decreasing? Give a reason for your answer.<\/p>\n\n\n\n

\"Description:<\/figure>\n\n\n\n

(c) Is there a time t, for 0 g t g 4, at which Brandon’s acceleration is equal to 2.5 miles per hour<\/p>\n\n\n\n

per hour? Justify your answer.<\/p>\n\n\n\n

\"Description:<\/figure>\n\n\n\n

(d) Is there a time t, for 0 < t=””>< 2,=”” at=”” which=”” brandon’s=”” velocity=”” is=”” equal=”” to=””><\/p>\n\n\n\n

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

(b) At time t=3t = 3, is Chloe’s speed increasing or decreasing? Give a reason for your answer.<\/h3>\n\n\n\n

To determine whether Chloe’s speed is increasing or decreasing at t=3t = 3, we need to evaluate two factors:<\/p>\n\n\n\n

    \n
  1. Chloe’s velocity (v(t)v(t))<\/strong> at t=3t = 3: If the velocity is positive, Chloe is moving forward; if negative, she’s moving backward.<\/li>\n\n\n\n
  2. Chloe’s acceleration (a(t)a(t))<\/strong> at t=3t = 3: Acceleration indicates whether velocity is increasing (positive a(t)a(t)) or decreasing (negative a(t)a(t)).<\/li>\n<\/ol>\n\n\n\n

    Speed increases when the velocity and acceleration have the same sign (both positive or both negative) and decreases when they have opposite signs.<\/p>\n\n\n\n

    \n\n\n\n

    (c) Is there a time tt, for 0\u2264t\u226440 \\leq t \\leq 4, at which Brandon’s acceleration is equal to 2.52.5 miles per hour per hour? Justify your answer.<\/h3>\n\n\n\n

    To answer this:<\/p>\n\n\n\n

      \n
    1. Determine Brandon’s acceleration function a(t)a(t)<\/strong>: a(t)a(t) is the derivative of Brandon’s velocity function v(t)v(t).<\/li>\n\n\n\n
    2. Analyze a(t)a(t) over 0\u2264t\u226440 \\leq t \\leq 4<\/strong>: Check whether a(t)a(t) attains the value 2.52.5 within the interval. Use the Intermediate Value Theorem (IVT) if a(t)a(t) is continuous.<\/li>\n<\/ol>\n\n\n\n

      Justification will involve showing the continuity of a(t)a(t) and verifying whether 2.52.5 lies within the range of a(t)a(t).<\/p>\n\n\n\n

      \n\n\n\n

      (d) Is there a time tt, for 0<t<20 < t < 2, at which Brandon’s velocity is equal to 0? Write the correct answer and provide a 300-word explanation.<\/h3>\n\n\n\n

      To solve:<\/p>\n\n\n\n

        \n
      1. Determine Brandon’s velocity function v(t)v(t)<\/strong>.<\/li>\n\n\n\n
      2. Find when v(t)=0v(t) = 0 in 0<t<20 < t < 2<\/strong>: Check for roots of v(t)v(t).<\/li>\n\n\n\n
      3. Use reasoning based on the continuity of v(t)v(t) and its behavior over the interval (0,2)(0, 2) to explain whether such a time tt exists.<\/li>\n<\/ol>\n\n\n\n

        The 300-word explanation would elaborate on these steps, referencing key properties of v(t)v(t) and any relevant theorems (e.g., Intermediate Value Theorem).<\/p>\n","protected":false},"excerpt":{"rendered":"

        b) At time t = 3, is Chloe’s speed increasing or decreasing? Give a reason for your answer. (c) Is there a time t, for 0 g t g 4, at which Brandon’s acceleration is equal to 2.5 miles per hour per hour? Justify your answer. (d) Is there a time t, for 0 < […]<\/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-181405","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/181405","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=181405"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/181405\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=181405"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=181405"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=181405"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}