{"id":28131,"date":"2025-06-20T10:22:41","date_gmt":"2025-06-20T10:22:41","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=28131"},"modified":"2025-06-20T10:22:44","modified_gmt":"2025-06-20T10:22:44","slug":"a-1400-kg-car-accelerates-uniformly-from-rest-to-60-mph-in-6-s","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-1400-kg-car-accelerates-uniformly-from-rest-to-60-mph-in-6-s\/","title":{"rendered":"A 1400 kg car accelerates uniformly from rest to 60 mph in 6 s"},"content":{"rendered":"\n<p>A 1400 kg car accelerates uniformly from rest to 60 mph in 6 s. Find the net force needed to produce this motion.<\/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>To find the <strong>net force<\/strong> required to accelerate the car, we use <strong>Newton\u2019s Second Law<\/strong> of motion: F=maF = ma<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>FF is the net force (in newtons, N),<\/li>\n\n\n\n<li>mm is the mass (in kilograms, kg),<\/li>\n\n\n\n<li>aa is the acceleration (in meters per second squared, m\/s\u00b2).<\/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\"><strong>Step 1: Convert speed from mph to m\/s<\/strong><\/h3>\n\n\n\n<p>Final speed = 60 mph<br>To convert to meters per second: 60&nbsp;mph=60\u00d70.44704=26.8224&nbsp;m\/s60 \\text{ mph} = 60 \\times 0.44704 = 26.8224 \\text{ m\/s}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Use acceleration formula<\/strong><\/h3>\n\n\n\n<p>The car starts from <strong>rest<\/strong>, so initial velocity u=0u = 0.<br>Time t=6t = 6 s<br>Final velocity v=26.8224&nbsp;m\/sv = 26.8224 \\text{ m\/s}<\/p>\n\n\n\n<p>Use the formula for acceleration: a=v\u2212ut=26.8224\u221206=4.4704&nbsp;m\/s2a = \\frac{v &#8211; u}{t} = \\frac{26.8224 &#8211; 0}{6} = 4.4704 \\text{ m\/s}^2<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Use Newton\u2019s Second Law<\/strong><\/h3>\n\n\n\n<p>Mass m=1400m = 1400 kg<br>Acceleration a=4.4704&nbsp;m\/s2a = 4.4704 \\text{ m\/s}^2 F=ma=1400\u00d74.4704=6258.56&nbsp;NF = ma = 1400 \\times 4.4704 = 6258.56 \\text{ N}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Final Answer:<\/strong><\/h3>\n\n\n\n<p>6258.6&nbsp;N(rounded&nbsp;to&nbsp;one&nbsp;decimal&nbsp;place)\\boxed{6258.6 \\text{ N}} \\quad (\\text{rounded to one decimal place})<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (300 words)<\/strong><\/h3>\n\n\n\n<p>To determine the net force required to accelerate a car, we use <strong>Newton\u2019s Second Law<\/strong>, which states that the net force acting on an object equals the product of its mass and acceleration. The problem provides the car&#8217;s mass as 1400 kg and specifies that the car starts from rest and reaches 60 mph in 6 seconds. However, since SI units are used in physics calculations, we must first convert 60 mph to meters per second. Using the conversion factor 1&nbsp;mph=0.44704&nbsp;m\/s1 \\text{ mph} = 0.44704 \\text{ m\/s}, 60 mph becomes approximately 26.82 m\/s.<\/p>\n\n\n\n<p>Next, we calculate acceleration using the formula a=\u0394vta = \\frac{\\Delta v}{t}, where \u0394v\\Delta v is the change in velocity and tt is the time. Since the car starts from rest, its initial velocity is 0, and the final velocity is 26.82 m\/s. Dividing this by the 6-second interval gives an acceleration of approximately 4.47 m\/s\u00b2.<\/p>\n\n\n\n<p>Now, applying Newton\u2019s Second Law F=maF = ma, we multiply the car\u2019s mass (1400 kg) by the calculated acceleration (4.47 m\/s\u00b2), resulting in a net force of 6258.6 newtons. This net force is what\u2019s required to uniformly accelerate the car from 0 to 60 mph in the given time. This value accounts only for the force to change velocity and doesn&#8217;t include resistance like friction or air drag, which would require even more force in real-world conditions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A 1400 kg car accelerates uniformly from rest to 60 mph in 6 s. Find the net force needed to produce this motion. The correct answer and explanation is: To find the net force required to accelerate the car, we use Newton\u2019s Second Law of motion: F=maF = ma Where: Step 1: Convert speed from [&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-28131","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28131","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=28131"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28131\/revisions"}],"predecessor-version":[{"id":28132,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28131\/revisions\/28132"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=28131"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=28131"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=28131"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}