{"id":210009,"date":"2025-04-29T15:58:51","date_gmt":"2025-04-29T15:58:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=210009"},"modified":"2025-04-29T15:58:53","modified_gmt":"2025-04-29T15:58:53","slug":"the-acceleration-due-to-gravity-is-9-8-meters-per-second-squared","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/29\/the-acceleration-due-to-gravity-is-9-8-meters-per-second-squared\/","title":{"rendered":"The acceleration due to gravity is -9.8 meters per second squared"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The acceleration due to gravity is -9.8 meters per second squared. An object is thrown upward from a 100-meter tower with a velocity of 49 meter per second.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> a. Find the velocity function. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b. Find the position function<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve this problem, we need to derive two functions for the object&#8217;s motion: the velocity function and the position function. We are given the following information:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial velocity ( v_0 = 49 \\, \\text{m\/s} )<\/li>\n\n\n\n<li>Initial position ( s_0 = 100 \\, \\text{m} )<\/li>\n\n\n\n<li>Acceleration due to gravity ( a = -9.8 \\, \\text{m\/s}^2 )<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">a. Velocity Function<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The velocity function ( v(t) ) describes how the velocity of the object changes over time. The acceleration ( a(t) ) is constant and is equal to ( -9.8 \\, \\text{m\/s}^2 ). To find the velocity function, we integrate the acceleration function with respect to time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The acceleration function is given by:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>a(t) = -9.8 \\, \\text{m\/s}^2<br>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since acceleration is the derivative of velocity, we integrate the acceleration function to find the velocity:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>v(t) = \\int a(t) \\, dt = \\int (-9.8) \\, dt = -9.8t + C<br>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To determine the constant ( C ), we use the initial condition that the velocity at ( t = 0 ) is ( v_0 = 49 \\, \\text{m\/s} ):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>v(0) = -9.8(0) + C = 49 \\quad \\Rightarrow \\quad C = 49<br>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the velocity function is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>v(t) = -9.8t + 49<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">b. Position Function<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The position function ( s(t) ) describes the object&#8217;s height above the ground at any given time. The velocity function is the derivative of the position function, so we can integrate the velocity function to find the position function.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>v(t) = \\frac{ds}{dt} = -9.8t + 49<br>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now, integrate the velocity function to find the position function:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>s(t) = \\int v(t) \\, dt = \\int (-9.8t + 49) \\, dt = -4.9t^2 + 49t + C_1<br>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To determine the constant ( C_1 ), we use the initial condition that the position at ( t = 0 ) is ( s_0 = 100 \\, \\text{m} ):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>s(0) = -4.9(0)^2 + 49(0) + C_1 = 100 \\quad \\Rightarrow \\quad C_1 = 100<br>]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the position function is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[<br>s(t) = -4.9t^2 + 49t + 100<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Velocity Function<\/strong>: ( v(t) = -9.8t + 49 )<\/li>\n\n\n\n<li><strong>Position Function<\/strong>: ( s(t) = -4.9t^2 + 49t + 100 )<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The velocity function ( v(t) = -9.8t + 49 ) shows that the object&#8217;s velocity decreases over time due to the negative acceleration caused by gravity. Initially, the object is moving upward at 49 m\/s, but the velocity gradually decreases as it moves against gravity. After reaching the peak, the object will start descending.<\/li>\n\n\n\n<li>The position function ( s(t) = -4.9t^2 + 49t + 100 ) shows the object&#8217;s height above the ground at any given time. It is a quadratic equation, with the initial height of the object being 100 meters and a positive initial velocity. As time progresses, the object moves upward, slows down, and eventually starts falling back toward the ground. The negative coefficient of ( t^2 ) indicates that gravity is pulling the object downward after it reaches its peak height.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>The acceleration due to gravity is -9.8 meters per second squared. An object is thrown upward from a 100-meter tower with a velocity of 49 meter per second. a. Find the velocity function. b. Find the position function The correct answer and explanation is : To solve this problem, we need to derive two functions [&hellip;]<\/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-210009","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/210009","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=210009"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/210009\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=210009"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=210009"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=210009"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}