{"id":6672,"date":"2024-04-15T02:32:25","date_gmt":"2024-04-15T02:32:25","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6672"},"modified":"2024-04-15T02:32:25","modified_gmt":"2024-04-15T02:32:25","slug":"if-the-angular-distance-0-2t3-3t2-the-angular-acceleration-at-t-1-sec-is-a-1-rad-sec2-b-4-rad-sec2-c-6-rad-sec2-d-12-rad-sec2","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-the-angular-distance-0-2t3-3t2-the-angular-acceleration-at-t-1-sec-is-a-1-rad-sec2-b-4-rad-sec2-c-6-rad-sec2-d-12-rad-sec2\/","title":{"rendered":"If the angular distance, 0 = 2t3 &#8211; 3t2, the angular acceleration at t = 1 sec. is A. 1 rad\/sec2 B. 4 rad\/sec2 C. 6 rad\/sec2 D. 12 rad\/sec2"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a9890cfc1b5c\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    1 rad\/sec2                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    4 rad\/sec2                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    6 rad\/sec2                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    12 rad\/sec2                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is $\\boxed{\\text{B}}$.<\/p>\n<p>The angular acceleration is the rate of change of angular velocity. It is calculated by taking the derivative of the angular velocity with respect to time. In this case, we are given that the angular distance is $0 = 2t^3 &#8211; 3t^2$. We can differentiate this equation to find the angular <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n            <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div>     <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> velocity:<\/p>\n<p>$$\\omega = \\frac{d}{dt} 0 = 6t^2 &#8211; 6t$$<\/p>\n<p>We can then differentiate the angular velocity equation to find the angular acceleration:<\/p>\n<p>$$\\alpha = \\frac{d}{dt} \\omega = 12t &#8211; 6$$<\/p>\n<p>We are asked to find the angular acceleration at $t = 1$ sec. Substituting this value into the angular acceleration equation, we get:<\/p>\n<p>$$\\alpha = 12(1) &#8211; 6 = 6 \\text{ rad\/sec}^2$$<\/p>\n<p>Therefore, the angular acceleration at $t = 1$ sec. is $\\boxed{\\text{B}}$, 6 rad\/sec$^2$.<\/p>\n<p>The other options are incorrect because they do not represent the correct value of the angular acceleration at $t = 1$ sec.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[645],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If the angular distance, 0 = 2t3 - 3t2, the angular acceleration at t = 1 sec. is A. 1 rad\/sec2 B. 4 rad\/sec2 C. 6 rad\/sec2 D. 12 rad\/sec2<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-angular-distance-0-2t3-3t2-the-angular-acceleration-at-t-1-sec-is-a-1-rad-sec2-b-4-rad-sec2-c-6-rad-sec2-d-12-rad-sec2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the angular distance, 0 = 2t3 - 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