{"id":782,"date":"2020-12-09T09:40:23","date_gmt":"2020-12-09T09:40:23","guid":{"rendered":"https:\/\/pickedshares.com\/?p=782"},"modified":"2021-02-05T11:23:23","modified_gmt":"2021-02-05T11:23:23","slug":"engineering-mechanics-3-exercise-1-uniformly-accelerated-movement","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-3-exercise-1-uniformly-accelerated-movement\/","title":{"rendered":"Uniformly accelerated movement"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Task<\/h3>\n\n\n\n<p>A car accelerates with a constant acceleration of a = 2,4 m\/s\u00b2. How long does it take for the car from 0 to 100 km\/h?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p>A solution video will be published soon <a href=\"http:\/\/www.youtube.com\/channel\/UCSh8qo2-6dhtbZqSLStt3Rg\" target=\"_blank\" rel=\"noreferrer noopener\">on this channel<\/a>.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>The given acceleration is the second derivation of x(t):<\/p>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n<p>\\[\\tag{1} \\ddot x(t) = a\\]<\/p>\n\n\n\n<p>Integrated once this yields the speed:<\/p>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n<p>\\[\\tag{2} \\int \\ddot x(t) dt \\xrightarrow{} \\dot x(t)\\]<\/p>\n<p>\\[\\tag{3} \\dot x(t) = at+c_1\\]<\/p>\n\n\n\n<p>The start condition for the moveme<\/p>\n\n\n\n<p>The boundary condition applies that the speed at time t = 0 is zero. The integration constant c<sub>1<\/sub> can thus be eliminated.<\/p>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n\n<p>\\[\\tag{4} \\dot x(t=0) = 0\\]<\/p>\n<p>\\[\\tag{5} c_1 = 0\\]<\/p>\n\n\n\n<p>Since the acceleration is given in m\/s\u00b2, the speed is also converted into m\/s.<\/p>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n\n<p>\\[\\tag{6} 100 km\/h = \\frac{ 100000m }{ 3600 s}\\]<\/p>\n<p>\\[\\tag{7} 100 km\/h = \\frac{ 500 m }{ 18 s}\\]<\/p>\n\n\n\n<p>We are looking for the value t for which the function gives the end speed of 100 km\/h:<\/p>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n\n<p>\\[\\tag{8} \\dot x(t=T) = \\frac{ 500m }{ 18 s}\\]<\/p>\n<p>\\[\\tag{9} \\frac{ 500m }{ 18s } = a T \\]<\/p>\n\n\n\n<p>with 2,4 m\/s\u00b2 for the accelerations it yields<\/p>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n\n<p>\\[\\tag{10} T = \\frac{ 500m }{ 18s \\cdot 2.4 \\frac{ m }{ s^2 }} \\]<\/p>\n<p>\\[\\tag{11} T = 11.57 s \\]<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Uniformly accelerated movement\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-3-exercise-1-uniformly-accelerated-movement\/\" aria-label=\"Read more about Uniformly accelerated movement\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":473,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[34,60],"tags":[25],"class_list":["post-782","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-iii","category-exercises","tag-kinematics","infinite-scroll-item","masonry-post","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-33"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Uniformly accelerated movement &#8226; pickedshares<\/title>\n<meta name=\"description\" content=\"A car shall be uniformly accelerated from 0 to 100 km\/h. 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