{"id":3264,"date":"2022-05-08T19:34:16","date_gmt":"2022-05-08T19:34:16","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=3264"},"modified":"2022-05-08T19:34:16","modified_gmt":"2022-05-08T19:34:16","slug":"derivation-of-kinetic-energy","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/05\/08\/derivation-of-kinetic-energy\/","title":{"rendered":"Derivation Of Kinetic Energy"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/mdr.foobrdigital.com\/wp-content\/uploads\/2022\/05\/Derivation-Of-Kinetic-Energy.png\" alt=\"\" class=\"wp-image-3265\" title=\"Derivation Of Kinetic Energy\"\/><\/figure>\n\n\n\n<p>The kinetic energy of a body is the energy that it possessed due to its motion. Kinetic energy can be defined as the work needed to accelerate an object of a given mass from rest to its stated velocity. The derivation of kinetic energy is one of the most common questions asked in the examination. Students must understand the kinetic energy derivation method properly to excel in their examination.<\/p>\n\n\n\n<p>Kinetic energy depends upon the velocity and the mass of the body. If the velocity of the body is zero, then the kinetic energy will also be zero. The derivation of\u00a0kinetic energy\u00a0is given below so that students can understand the concept more effectively. The kinetic energy formula derivation can be done using algebra and calculus. Both the methods are explained below.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Derivation of Kinetic Energy using Algebra<\/h2>\n\n\n\n<p>The kinetic energy derivation using only algebra is one of the best ways to understand the formula in-depth.<\/p>\n\n\n\n<p>Starting with the work-energy theorem and then adding Newton\u2019s second law of motion we can say that,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2018\/11\/physics\/wp-content\/uploads\/2018\/06\/Derivation-Of-Kinetic-Energy-1.png\" alt=\"Derivation Of Kinetic Energy\" title=\"Derivation Of Kinetic Energy\"\/><\/figure>\n\n\n\n<p>Now, taking the kinematics equation and rearranging it, we get<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2018\/11\/physics\/wp-content\/uploads\/2018\/06\/Derivation-Of-Kinetic-Energy-2.png\" alt=\"Derivation Of Kinetic Energy\" title=\"Derivation Of Kinetic Energy\"\/><\/figure>\n\n\n\n<p>Combining the 2 expressions we get,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2018\/11\/physics\/wp-content\/uploads\/2018\/06\/Derivation-Of-Kinetic-Energy-3.png\" alt=\"Derivation Of Kinetic Energy\" title=\"Derivation Of Kinetic Energy\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2018\/11\/physics\/wp-content\/uploads\/2018\/06\/Derivation-Of-Kinetic-Energy-4.png\" alt=\"Derivation Of Kinetic Energy\" title=\"Derivation Of Kinetic Energy\"\/><\/figure>\n\n\n\n<p>Now we already know that kinetic energy is the energy that it possessed due to its motion. So the kinetic energy at rest should be zero. Therefore, we can say that kinetic energy is:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2018\/11\/physics\/wp-content\/uploads\/2018\/06\/Derivation-Of-Kinetic-Energy-5.png\" alt=\"Derivation Of Kinetic Energy\" title=\"Derivation Of Kinetic Energy\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Derivation of Kinetic Energy using Calculus<\/h2>\n\n\n\n<p>The derivation of kinetic energy using calculus is given below. To derive an expression for kinetic energy using calculus, we will not need to assume anything about the acceleration.<\/p>\n\n\n\n<p>Starting with the work-energy theorem and\u00a0Newton\u2019s second law of motion\u00a0we can say that<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2018\/11\/physics\/wp-content\/uploads\/2018\/06\/Derivation-Of-Kinetic-Energy-6.png\" alt=\"Derivation Of Kinetic Energy\" title=\"Derivation Of Kinetic Energy\"\/><\/figure>\n\n\n\n<p>Now rearranging the differential terms to get the function and the integral into an agreement.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2018\/11\/physics\/wp-content\/uploads\/2018\/06\/Derivation-Of-Kinetic-Energy-7.png\" alt=\"Derivation Of Kinetic Energy\" title=\"Derivation Of Kinetic Energy\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2018\/11\/physics\/wp-content\/uploads\/2018\/06\/Derivation-Of-Kinetic-Energy-8.png\" alt=\"Derivation Of Kinetic Energy\" title=\"Derivation Of Kinetic Energy\"\/><\/figure>\n\n\n\n<p>Now, we know that the kinetic energy of a body at rest is zero. So we can say that the kinetic energy is:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2018\/11\/physics\/wp-content\/uploads\/2018\/06\/Derivation-Of-Kinetic-Energy-9.png\" alt=\"Derivation Of Kinetic Energy\" title=\"Derivation Of Kinetic Energy\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The kinetic energy of a body is the energy that it possessed due to its motion. Kinetic energy can be defined as the work needed to accelerate an object of a given mass from rest to its stated velocity. The derivation of kinetic energy is one of the most common questions asked in the examination. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[665],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3264"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=3264"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3264\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=3264"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=3264"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=3264"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}