{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T17:24:06+00:00","modifiedTime":"2021-09-09T20:05:03+00:00","timestamp":"2022-09-14T18:18:37+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Science","_links":{"self":"//dummies-api.dummies.com/v2/categories/33756"},"slug":"science","categoryId":33756},{"name":"Physics","_links":{"self":"//dummies-api.dummies.com/v2/categories/33769"},"slug":"physics","categoryId":33769}],"title":"How to Calculate Time and Distance from Acceleration and Velocity","strippedTitle":"how to calculate time and distance from acceleration and velocity","slug":"how-to-calculate-time-and-distance-from-acceleration-and-velocity","canonicalUrl":"","seo":{"metaDescription":"Learn how to calculate time and distance when you know the acceleration and velocity with this concise, straightforward explanation.","noIndex":0,"noFollow":0},"content":"In a physics equation, given a constant <a href=\"//www.dummies.com/education/science/physics/how-to-calculate-acceleration/\" target=\"_blank\" rel=\"noopener\">acceleration</a> and the change in velocity of an object, you can figure out both the <a href=\"//www.dummies.com/education/math/basic-math/calculating-speed-time-and-distance/\" target=\"_blank\" rel=\"noopener\">time involved and the distance traveled</a>. For instance, imagine you’re a drag racer. Your acceleration is 26.6 meters per second<sup>2</sup>, and your final speed is 146.3 meters per second. Now find the total distance traveled. Got you, huh? “Not at all,” you say, supremely confident. “Just let me get my calculator.”\r\n\r\nYou know the acceleration and the final speed, and you want to know the total distance required to get to that speed. This problem looks like a puzzler, but if you need the time, you can always solve for it. You know the final speed, <i>v</i><i><sub>f</sub></i>,<i> </i>and the initial speed, <i>v</i><i><sub>i</sub></i> (which is zero), and you know the acceleration, <i>a</i><i>.</i> Because <i>v</i><i><sub>f</sub></i><i> – v</i><i><sub>i</sub></i><i> = at</i><i>, </i>you know that\r\n\r\n<img src=\"//sg.cdnki.com/what-is-the-time-interval-of-acceleration---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzMyOTgzNy5pbWFnZTAucG5n.webp\" alt=\"image0.png\" width=\"136\" height=\"115\" />\r\n\r\nNow you have the time. You still need the distance, and you can get it this way:\r\n\r\n<img src=\"//sg.cdnki.com/what-is-the-time-interval-of-acceleration---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzMyOTgzOC5pbWFnZTEucG5n.webp\" alt=\"image1.png\" width=\"93\" height=\"37\" />\r\n\r\nThe second term drops out because <i>v</i><i><sub>i</sub></i> = 0, so all you have to do is plug in the numbers:\r\n\r\n<img src=\"//sg.cdnki.com/what-is-the-time-interval-of-acceleration---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzMyOTgzOS5pbWFnZTIucG5n.webp\" alt=\"image2.png\" width=\"173\" height=\"107\" />\r\n\r\nIn other words, the total distance traveled is 402 meters, or a quarter mile. Must be a quarter-mile racetrack.","description":"In a physics equation, given a constant <a href=\"//www.dummies.com/education/science/physics/how-to-calculate-acceleration/\" target=\"_blank\" rel=\"noopener\">acceleration</a> and the change in velocity of an object, you can figure out both the <a href=\"//www.dummies.com/education/math/basic-math/calculating-speed-time-and-distance/\" target=\"_blank\" rel=\"noopener\">time involved and the distance traveled</a>. For instance, imagine you’re a drag racer. Your acceleration is 26.6 meters per second<sup>2</sup>, and your final speed is 146.3 meters per second. Now find the total distance traveled. Got you, huh? “Not at all,” you say, supremely confident. “Just let me get my calculator.”\r\n\r\nYou know the acceleration and the final speed, and you want to know the total distance required to get to that speed. This problem looks like a puzzler, but if you need the time, you can always solve for it. You know the final speed, <i>v</i><i><sub>f</sub></i>,<i> </i>and the initial speed, <i>v</i><i><sub>i</sub></i> (which is zero), and you know the acceleration, <i>a</i><i>.</i> Because <i>v</i><i><sub>f</sub></i><i> – v</i><i><sub>i</sub></i><i> = at</i><i>, </i>you know that\r\n\r\n<img src=\"//www.dummies.com/wp-content/uploads/329837.image0.png\" alt=\"image0.png\" width=\"136\" height=\"115\" />\r\n\r\nNow you have the time. You still need the distance, and you can get it this way:\r\n\r\n<img src=\"//www.dummies.com/wp-content/uploads/329838.image1.png\" alt=\"image1.png\" width=\"93\" height=\"37\" />\r\n\r\nThe second term drops out because <i>v</i><i><sub>i</sub></i> = 0, so all you have to do is plug in the numbers:\r\n\r\n<img src=\"//www.dummies.com/wp-content/uploads/329839.image2.png\" alt=\"image2.png\" width=\"173\" height=\"107\" />\r\n\r\nIn other words, the total distance traveled is 402 meters, or a quarter mile. Must be a quarter-mile racetrack.","blurb":"","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":" <p><b> Dr. Steven Holzner</b> has written more than 40 books about physics and programming. He was a contributing editor at <i>PC Magazine</i> and was on the faculty at both MIT and Cornell. He has authored Dummies titles including <i>Physics For Dummies</i> and <i>Physics Essentials For Dummies.</i> Dr. Holzner received his PhD at Cornell.</p> ","hasArticle":false,"_links":{"self":"//dummies-api.dummies.com/v2/authors/8967"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"//dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/208460"}},{"articleId":184049,"title":"A List of Physics Constants","slug":"a-list-of-physics-constants","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/184049"}},{"articleId":184043,"title":"Physics Equations and Formulas","slug":"physics-equations-and-formulas","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/184043"}},{"articleId":174308,"title":"Calculating Tangential Velocity on a Curve","slug":"calculating-tangential-velocity-on-a-curve","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/174308"}},{"articleId":174307,"title":"Flowing from Hot to Cold: The Second Law of Thermodynamics","slug":"flowing-from-hot-to-cold-the-second-law-of-thermodynamics","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/174307"}}],"fromCategory":[{"articleId":209405,"title":"String Theory For Dummies Cheat Sheet","slug":"string-theory-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/209405"}},{"articleId":209012,"title":"Physics II For Dummies Cheat Sheet","slug":"physics-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/209012"}},{"articleId":208592,"title":"Thermodynamics For Dummies Cheat Sheet","slug":"thermodynamics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/208592"}},{"articleId":208578,"title":"Optics For Dummies Cheat Sheet","slug":"optics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/208578"}},{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/208460"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282467,"slug":"physics-i-for-dummies","isbn":"9781119872221","categoryList":["academics-the-arts","science","physics"],"amazon":{"default":"//www.amazon.com/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"//www.amazon.ca/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"//www.tkqlhce.com/click-9208661-13710633?url=//www.chapters.indigo.ca/en-ca/books/product/1119872227-item.html&cjsku=978111945484","gb":"//www.amazon.co.uk/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"//www.amazon.de/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"//www.dummies.com/wp-content/uploads/9781119872221-203x255.jpg","width":203,"height":255},"title":"Physics I For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"<p><b> Dr. <b data-author-id=\"8967\">Steven Holzner</b></b> has written more than 40 books about physics and programming. He was a contributing editor at <i>PC Magazine</i> and was on the faculty at both MIT and Cornell. He has authored Dummies titles including <i>Physics For Dummies</i> and <i>Physics Essentials For Dummies.</i> Dr. Holzner received his PhD at Cornell.</p>","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":" <p><b> Dr. Steven Holzner</b> has written more than 40 books about physics and programming. He was a contributing editor at <i>PC Magazine</i> and was on the faculty at both MIT and Cornell. He has authored Dummies titles including <i>Physics For Dummies</i> and <i>Physics Essentials For Dummies.</i> Dr. Holzner received his PhD at Cornell.</p> ","hasArticle":false,"_links":{"self":"//dummies-api.dummies.com/v2/authors/8967"}}],"_links":{"self":"//dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","science","physics"]},{"key":"isbn","values":["9781119872221"]}]\" id=\"du-slot-63221afd0e9e2\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","science","physics"]},{"key":"isbn","values":["9781119872221"]}]\" 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You know the acceleration and the final speed, and you want to know the total distance required to get to that speed. This problem looks like a puzzler, but if you need the time, you can always solve for it. You know the final speed, vf, and the initial speed, vi (which is zero), and you know the acceleration, a. Because vf – vi = at, you know that
Now you have the time. You still need the distance, and you can get it this way:
The second term drops out because vi = 0, so all you have to do is plug in the numbers:
In other words, the total distance traveled is 402 meters, or a quarter mile. Must be a quarter-mile racetrack.