{"id":243175,"date":"2025-07-04T12:47:49","date_gmt":"2025-07-04T12:47:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=243175"},"modified":"2025-07-04T12:47:51","modified_gmt":"2025-07-04T12:47:51","slug":"derive-the-equation-for-the-kinetic-energy-of-an-object-of-mass-m-moving-with-velocity-v","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/04\/derive-the-equation-for-the-kinetic-energy-of-an-object-of-mass-m-moving-with-velocity-v\/","title":{"rendered":"Derive the equation for the kinetic energy of an object of mass m’ moving with velocity v."},"content":{"rendered":"\n

Derive the equation for the kinetic energy of an object of mass m’ moving with velocity v.<\/p>\n\n\n\n

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

To derive the equation for the kinetic energy of an object of mass m<\/strong> moving with velocity v<\/strong>, we start from the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.<\/p>\n\n\n\n

Step 1: Definition of Work<\/h3>\n\n\n\n

Work (W<\/strong>) is defined as the force (F<\/strong>) applied on an object times the distance (d<\/strong>) over which the force is applied. Mathematically:W=F\u22c5dW = F \\cdot dW=F\u22c5d<\/p>\n\n\n\n

Now, consider a scenario where an object starts from rest and moves under the influence of a constant force. The force is related to the object’s acceleration (a<\/strong>) by Newton\u2019s second law:F=m\u22c5aF = m \\cdot aF=m\u22c5a<\/p>\n\n\n\n

where m<\/strong> is the mass of the object and a<\/strong> is the acceleration.<\/p>\n\n\n\n

Step 2: Relating Velocity and Acceleration<\/h3>\n\n\n\n

Since the object is accelerating, we can use the kinematic equation that relates velocity and acceleration:v2=u2+2adv^2 = u^2 + 2adv2=u2+2ad<\/p>\n\n\n\n

where v<\/strong> is the final velocity, u<\/strong> is the initial velocity (which is 0 in this case, as we are considering motion from rest), a<\/strong> is acceleration, and d<\/strong> is the distance traveled. Substituting u = 0<\/strong>, the equation simplifies to:v2=2adv^2 = 2adv2=2ad<\/p>\n\n\n\n

Now, solving for d<\/strong>, we get:d=v22ad = \\frac{v^2}{2a}d=2av2\u200b<\/p>\n\n\n\n

Step 3: Work Done<\/h3>\n\n\n\n

Now substitute this expression for d<\/strong> into the formula for work:W=F\u22c5d=(m\u22c5a)\u22c5v22aW = F \\cdot d = (m \\cdot a) \\cdot \\frac{v^2}{2a}W=F\u22c5d=(m\u22c5a)\u22c52av2\u200b<\/p>\n\n\n\n

The acceleration terms cancel out, and we get:W=12mv2W = \\frac{1}{2} m v^2W=21\u200bmv2<\/p>\n\n\n\n

Step 4: Kinetic Energy<\/h3>\n\n\n\n

Since the work done on the object is equal to the change in its kinetic energy, we conclude that the kinetic energy (KE<\/strong>) of an object of mass m<\/strong> moving with velocity v<\/strong> is:KE=12mv2KE = \\frac{1}{2} m v^2KE=21\u200bmv2<\/p>\n\n\n\n

This is the equation for kinetic energy. It shows that the kinetic energy of an object depends on its mass and the square of its velocity.<\/p>\n\n\n\n

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

Derive the equation for the kinetic energy of an object of mass m’ moving with velocity v. The Correct Answer and Explanation is: To derive the equation for the kinetic energy of an object of mass m moving with velocity v, we start from the work-energy principle. According to this principle, the work done on […]<\/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-243175","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/243175","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=243175"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/243175\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=243175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=243175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=243175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}