{"id":1591,"date":"2013-06-07T11:51:43","date_gmt":"2013-06-07T11:51:43","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=1591"},"modified":"2026-03-28T11:21:54","modified_gmt":"2026-03-28T16:21:54","slug":"displacement","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/displacement\/","title":{"rendered":"Displacement in Physics"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_fryix3XdtYQ\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_fryix3XdtYQ\" data-source-videoID=\"fryix3XdtYQ\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Displacement in Physics Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Displacement in Physics\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_fryix3XdtYQ:hover {cursor:pointer;} img#videoThumbnailImage_fryix3XdtYQ {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/674-Displacement-in-Physics-2-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_fryix3XdtYQ\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_fryix3XdtYQ\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Displacement in Physics\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_fryix3XdtYQ\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_fryix3XdtYQ\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_fryix3XdtYQ\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction ZLB_Function() {\n  var x = document.getElementById(\"ZLB\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"ZLB_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"ZLB\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Displacement_Formula\" class=\"smooth-scroll\">Displacement Formula<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Determining_Total_Distance\" class=\"smooth-scroll\">Determining Total Distance<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Direction_of_Displacement\" class=\"smooth-scroll\">Direction of Displacement<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Review\" class=\"smooth-scroll\">Review<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Today, we\u2019re going to look at what displacement is and how it relates to \u201ctotal distance\u201d.<\/p>\n<h2><span id=\"Displacement_Formula\" class=\"m-toc-anchor\"><\/span>Displacement Formula<\/h2>\n<p>\nDisplacement happens when an object moves from one location to another. The general equation for displacement is:<\/p>\n<div class=\"examplesentence\">\\(\\text{displacement} = \\text{final position} &#8211; \\text{initial position}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe most important part of displacement is noting that the path we take to get from one location to another does not matter. We only need to know where we started and where we ended up.<\/p>\n<p>Sometimes we call displacement an \u201cas the crow flies\u201d measurement, meaning a crow flies directly from one place to another using the shortest path possible. Similarly, displacement tells us the shortest distance from an initial location to a final location.<\/p>\n<h2><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h2>\n<p>\nLet\u2019s look at skiing for example. A group of skiers will start at the top of the mountain. One skier really likes adventure, so she zigs and zags all around the mountain as she skis down the hill. This skier loves going as fast as possible, so he zips straight down from the ski lift to the bottom. This last skier sees that the slope is a lot steeper than she thought, so she takes the lift back down. We consider the top of the mountain the initial position and the bottom of the mountain the final position. All the skiers took different paths to get from the top of the mountain to the bottom of the mountain, but their displacement is exactly the same.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/02\/displacement-1.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\"  \/><\/p>\n<h2><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h2>\n<p>\nAnother example is Jackie Joyner-Kersee\u2019s world record long jump. Her initial position is a line she runs to and begins her jump from. Her final position was 7.40 meters away. The jump was a straight line across the ground, but she jumped over the ground in an arc. The world record doesn\u2019t care about how high off the ground she was; it only considers her starting and final positions.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/02\/displacement-2.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" style=\"box-shadow: 1.5px 1.5px 3px gray;\"  \/><\/p>\n<h2><span id=\"Determining_Total_Distance\" class=\"m-toc-anchor\"><\/span>Determining Total Distance<\/h2>\n<p>\nBut what if you want <strong>total distance<\/strong>? A car\u2019s odometer tells us how far the car has traveled in total. It is a measure of displacement that takes the path into account by breaking the path into tiny pieces. For example, it\u2019s two miles to grandma\u2019s house if we went directly through the forest on a straight path. But our car\u2019s odometer says we traveled three miles. We have to go over a bridge and along a winding road, so the distance we\u2019ve traveled is three miles, even though our displacement is less.<\/p>\n<h2><span id=\"Direction_of_Displacement\" class=\"m-toc-anchor\"><\/span>Direction of Displacement<\/h2>\n<p>\nSometimes we want to specify not just the total displacement, but also the direction of the displacement. These two pieces of information, when used together, form what is called a <strong>vector<\/strong>. A vector gives us the magnitude and a direction. The magnitude is the total displacement and the direction is an arrow pointing from the initial location to the final location.<\/p>\n<p>A common example is giving a friend directions from their house to yours. Consider these directions: \u201cGo left, then go right, then you will be at my house.\u201d We can\u2019t use these directions, because they don\u2019t include a total displacement! But what if your friend said, \u201cGo three blocks, then go four blocks, then go seven blocks.\u201d? That\u2019s not enough information either! There are no directions to turn! We need vectors; a direction to turn and how long to travel in that direction.<\/p>\n<hr>\n<h2><span id=\"Review\" class=\"m-toc-anchor\"><\/span>Review<\/h2>\n<p>\nBefore we go, let\u2019s wrap up with a review question:<\/p>\n<p>In flyball, dogs take turns running down a track, grabbing a ball, then running back to the start, like a relay race. If the track is 100 meters long, what is the total displacement of the four-dog team?<\/p>\n<ol style=\"list-style: upper-alpha;\">\n<li>400 meters<\/li>\n<li>800 meters<\/li>\n<li>0 meters<\/li>\n<li>It depends on the breed of the dogs<\/li>\n<\/ol>\n<div style=\"text-align: center; margin-bottom: 20px;\"><button class=\"buttontranscript\" onClick=\"toggle('Answer1')\">Show Answer<\/button><\/div>\n<div id=\"Answer1\" style=\"display:none; box-shadow: 1.5px 1.5px 5px grey; background-color:#E0E0E0; padding: 30px; padding-bottom: 15px; width: 60%; margin: auto; text-align: center;\">\n<strong>The answer is 0 meters!<\/strong><\/p>\n<p style=\"text-align: left;\">Each dog starts and stops at the same location. Remember that displacement doesn\u2019t take the path into account.<\/p>\n<\/div>\n<p>\n&nbsp;<br \/>\nThanks for watching, and happy studying!<\/p>\n<ul class=\"citelist\">\n<li><a href=\"https:\/\/www.velonews.com\/2018\/07\/tour-de-france\/2018-tour-de-france-numbers_471423\"target=\"_blank\">VeloNews.com. 2018. \u201cThe 2018 Tour de France, by the Numbers.\u201d<\/a><\/li>\n<li><a href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/posit.html\"target=\"_blank\">\u201cPosition and Displacement.\u201d n.d. Hyperphysics.phy-Astr.gsu.edu<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Flyball\"target=\"_blank\">\u201cFlyball.\u201d 2023. Wikipedia<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Jackie_Joyner-Kersee\"target=\"_blank\">\u201cJackie Joyner-Kersee.\u201d 2022. Wikipedia<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/physics\/\">Return to Physics Videos<\/a><\/p>\n<\/div>\n<p><script>\nfunction toggle(obj) {\n          var obj=document.getElementById(obj);\n          if (obj.style.display == \"block\") obj.style.display = \"none\";\n          else obj.style.display = \"block\";\n}\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Return to Physics Videos<\/p>\n","protected":false},"author":1,"featured_media":99667,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-1591","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-physics-basics-videos","7":"page_category-physics-motion-videos","8":"page_type-video","9":"subject_matter-science"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/1591","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=1591"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/1591\/revisions"}],"predecessor-version":[{"id":260932,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/1591\/revisions\/260932"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/99667"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=1591"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}