A boat moves slowly out of a marina (so as to not leave a wake) with a speed of 1.50 m\/s. As soon as it passes the breakwater, leaving the marina, it throttles up and accelerates at 2.40 m\/s\/s.
a) How fast is the boat moving after accelerating for 5 seconds?
b) How far did the boat travel during that time?<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n We will use kinematic equations to solve this problem.<\/p>\n\n\n\n Using the kinematic equation:<\/p>\n\n\n\n [ [ [ So, the boat’s velocity after 5 seconds is 13.50 m\/s<\/strong>.<\/p>\n\n\n\n Using the kinematic equation:<\/p>\n\n\n\n [ [ [ [ [ So, the boat travels 37.50 meters<\/strong> during this time.<\/p>\n\n\n\n The boat initially moves at a slow speed of 1.50 m\/s to avoid making a wake in the marina. As soon as it exits the breakwater, it starts accelerating at 2.40 m\/s\u00b2. To determine how fast it is moving after 5 seconds, we use the equation ( v_f = v_i + at ), which accounts for the constant acceleration over time. This gives us a final velocity of 13.50 m\/s.<\/p>\n\n\n\n To find the distance traveled, we use the equation ( s = v_i t + \\frac{1}{2} a t^2 ), which considers both the initial motion and the effect of acceleration. The boat covers 37.50 meters in 5 seconds. These calculations show how acceleration significantly increases both speed and distance traveled over time.<\/p>\n","protected":false},"excerpt":{"rendered":" A boat moves slowly out of a marina (so as to not leave a wake) with a speed of 1.50 m\/s. As soon as it passes the breakwater, leaving the marina, it throttles up and accelerates at 2.40 m\/s\/s.a) How fast is the boat moving after accelerating for 5 seconds?b) How far did the boat […]<\/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-203226","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/203226","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=203226"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/203226\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=203226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=203226"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=203226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Given Data:<\/h3>\n\n\n\n
\n
(a) Final Velocity after 5 seconds<\/strong><\/h4>\n\n\n\n
v_f = v_i + at
]<\/p>\n\n\n\n
v_f = 1.50 + (2.40 \\times 5.00)
]<\/p>\n\n\n\n
v_f = 1.50 + 12.00 = 13.50 \\text{ m\/s}
]<\/p>\n\n\n\n(b) Distance Traveled<\/strong><\/h4>\n\n\n\n
s = v_i t + \\frac{1}{2} a t^2
]<\/p>\n\n\n\n
s = (1.50 \\times 5.00) + \\frac{1}{2} (2.40) (5.00)^2
]<\/p>\n\n\n\n
s = 7.50 + \\frac{1}{2} (2.40) (25)
]<\/p>\n\n\n\n
s = 7.50 + (1.20 \\times 25)
]<\/p>\n\n\n\n
s = 7.50 + 30.00 = 37.50 \\text{ m}
]<\/p>\n\n\n\nExplanation:<\/strong><\/h3>\n\n\n\n