{"id":6702,"date":"2024-04-15T02:32:52","date_gmt":"2024-04-15T02:32:52","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=6702"},"modified":"2024-04-15T02:32:52","modified_gmt":"2024-04-15T02:32:52","slug":"the-motion-of-a-particle-is-described-by-the-relation-x-t2-10t-30-where-x-is-in-meters-and-t-in-seconds-the-total-distance-travelled-by-the-particle-from-t-0-to-t-10-seconds-would-be-a-ze","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-motion-of-a-particle-is-described-by-the-relation-x-t2-10t-30-where-x-is-in-meters-and-t-in-seconds-the-total-distance-travelled-by-the-particle-from-t-0-to-t-10-seconds-would-be-a-ze\/","title":{"rendered":"The motion of a particle is described by the relation x = t2 &#8211; 10t + 30, where x is in meters and t in seconds. The total distance travelled by the particle from t = 0 to t = 10 seconds would be A. Zero B. 30 m C. 50 m D. 60 m"},"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_6a9a59140ff84\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    Zero                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    30 m                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    50 m                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    60 m                <\/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 C. 50 m.<\/p>\n<p>The total distance traveled by a particle is the integral of its speed over time. The speed of a particle is the rate of change of its position, which is given by the derivative of its position with respect to time. In this case, the position of the particle is given by the equation $x = t^2 &#8211; 10t + 30$, so the speed is given by $v = \\frac{d}{dt} x = 2t &#8211; 10$.<\/p>\n<p>To find the total distance traveled by the particle from $t = 0$ to $t = 10$, we need to integrate the speed from $t = 0$ to $t = 10$. This gives us<\/p>\n<p>$$\\int_0^{10} v(t) dt = \\int_0^{10} (2t &#8211; 10) dt = t^2 &#8211; 5t + 30|_0^{10} = 100 &#8211; 50 + 30 = 50.$$<\/p>\n<p>Therefore, the total distance traveled by the particle from $t = 0$ to $t = 10$ is 50 meters.<\/p>\n<p>Option A is incorrect because <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                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> the particle is moving at all times, so it must have traveled some distance. Option B is incorrect because the particle is moving in a positive direction, so it cannot have traveled a <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> negative distance. Option D is incorrect because the particle is moving in a positive direction, so it cannot have traveled a distance of 60 meters.<\/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>The motion of a particle is described by the relation x = t2 - 10t + 30, where x is in meters and t in seconds. The total distance travelled by the particle from t = 0 to t = 10 seconds would be A. 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