{"id":18913,"date":"2025-06-13T11:14:42","date_gmt":"2025-06-13T11:14:42","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=18913"},"modified":"2025-06-13T11:16:40","modified_gmt":"2025-06-13T11:16:40","slug":"a-person-drives-an-automobile-with-a-mass-of-450-kilograms-at-a-velocity-of-26-meters-per-second","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-person-drives-an-automobile-with-a-mass-of-450-kilograms-at-a-velocity-of-26-meters-per-second\/","title":{"rendered":"A person drives an automobile with a mass of 450 kilograms at a velocity of 26 meters per second"},"content":{"rendered":"\n<p>A person drives an automobile with a mass of 450 kilograms at a velocity of 26 meters per second. The driver accelerates to a velocity of 30 meters per second. The difference in the automobile\u2019s kinetic energy between the two velocities is joules. You may use the calculator.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>Let&#8217;s solve the problem step by step.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Given data:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mass, m=450\u2009kgm = 450 \\, \\text{kg}<\/li>\n\n\n\n<li>Initial velocity, v1=26\u2009m\/sv_1 = 26 \\, \\text{m\/s}<\/li>\n\n\n\n<li>Final velocity, v2=30\u2009m\/sv_2 = 30 \\, \\text{m\/s}<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Write down the kinetic energy formula:<\/h3>\n\n\n\n<p>KE=12mv2KE = \\frac{1}{2} m v^2<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate initial kinetic energy:<\/h3>\n\n\n\n<p>KE1=12\u00d7450\u00d7(26)2=225\u00d7676=152,100\u2009JoulesKE_1 = \\frac{1}{2} \\times 450 \\times (26)^2 = 225 \\times 676 = 152,100 \\, \\text{Joules}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate final kinetic energy:<\/h3>\n\n\n\n<p>KE2=12\u00d7450\u00d7(30)2=225\u00d7900=202,500\u2009JoulesKE_2 = \\frac{1}{2} \\times 450 \\times (30)^2 = 225 \\times 900 = 202,500 \\, \\text{Joules}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Find the difference in kinetic energy:<\/h3>\n\n\n\n<p>\u0394KE=KE2\u2212KE1=202,500\u2212152,100=50,400\u2009Joules\\Delta KE = KE_2 &#8211; KE_1 = 202,500 &#8211; 152,100 = 50,400 \\, \\text{Joules}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Answer:<\/strong><\/h3>\n\n\n\n<p>The difference in the automobile\u2019s kinetic energy between the two velocities is <strong>50,400 Joules<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Kinetic energy (KE) is the energy possessed by an object due to its motion. It depends on both the mass of the object and the square of its velocity, following the formula KE=12mv2KE = \\frac{1}{2} m v^2. When the velocity of an object changes, its kinetic energy changes accordingly.<\/p>\n\n\n\n<p>In this problem, the automobile\u2019s velocity increases from 26 m\/s to 30 m\/s. Even though this change might seem small, because kinetic energy depends on the square of velocity, the energy difference can be substantial.<\/p>\n\n\n\n<p>First, we calculate the kinetic energy at the initial velocity (26 m\/s), then the kinetic energy at the final velocity (30 m\/s). The difference between these two values represents the energy added to the car to increase its speed.<\/p>\n\n\n\n<p>This difference in kinetic energy (50,400 Joules) essentially tells us how much work (energy) the engine must supply to accelerate the vehicle from 26 m\/s to 30 m\/s, neglecting other forces like friction or air resistance. Understanding this energy change is crucial in physics and engineering to analyze the performance and fuel efficiency of vehicles.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A person drives an automobile with a mass of 450 kilograms at a velocity of 26 meters per second. The driver accelerates to a velocity of 30 meters per second. The difference in the automobile\u2019s kinetic energy between the two velocities is joules. You may use the calculator. The correct answer and explanation is: Let&#8217;s [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-18913","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18913","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=18913"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18913\/revisions"}],"predecessor-version":[{"id":18914,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18913\/revisions\/18914"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=18913"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=18913"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=18913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}