{"id":5660,"date":"2019-11-07T13:35:48","date_gmt":"2019-11-07T08:05:48","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=5660"},"modified":"2022-11-04T12:06:29","modified_gmt":"2022-11-04T06:36:29","slug":"what-is-velocity-time-graph","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/what-is-velocity-time-graph\/","title":{"rendered":"What is Velocity time graph?"},"content":{"rendered":"<hr \/>\n<h2 style=\"text-align: center;\"><span style=\"color: #800000;\"><strong>Velocity vs Time graph<\/strong><\/span><\/h2>\n<hr \/>\n<p>This article is about the velocity-time graph. Before going further details of the topic let us first understand how to draw these graphs. To draw graphs in x-y- plane<\/p>\n<ul>\n<li>The independent variable is always taken on the x-axis.<\/li>\n<li>We plot the dependent variable on the y-axis.<\/li>\n<li>The dependent variable is dependent on the independent variable through some function. Know more about <a href=\"https:\/\/physicscatalyst.com\/maths\/functions-in-maths.php\"  rel=\"noopener noreferrer\">Functions in Maths<\/a><\/li>\n<\/ul>\n<p>Let us observe the case of <a href=\"https:\/\/physicscatalyst.com\/mech\/kinematic-equations-for-uniformly-accelerated-motion.php\"  rel=\"noopener noreferrer\">Kinematic equations for uniformly accelerated Motion<\/a>. Time is our fundamental independent variable and position is a dependent variable. Along with position, displacement, velocity, and acceleration are also dependent variables. There are three basic types of motion graphs<\/p>\n<ol>\n<li><a href=\"https:\/\/physicscatalyst.com\/article\/position-time-graph\/\">Position-Time Graph<\/a> (x-t graph)<\/li>\n<li>Velocity-Time Graph (v-t graph)<\/li>\n<li>Acceleration-Time Graph<\/li>\n<\/ol>\n<hr \/>\n<p>The velocity-time graph is the graph plotted between the velocity of a particle with the passage of time. These graphs are very useful as we can extract various kinds of information from a given v-t graph.<\/p>\n<ul>\n<li>Velocity and speed of the particle at any instant of time can be found easily from v-t plot.<\/li>\n<li>From the v-t graph, we can also find the distance traveled by the particle.<\/li>\n<li>We can also find average speed and average velocity for any time interval from the v-t plot.<\/li>\n<li>The slope of velocity vs time graph gives the acceleration of the moving body.<\/li>\n<\/ul>\n<h3>Velocity-time graph uniform motion<\/h3>\n<p>A body is said to have uniform motion if it covers equal distance in an equal amount of time. In other words, we can say that a body has uniform motion if it moves with a fixed velocity \\(\\vec v\\) in the same fixed direction.<br \/>\nThe figure given below shows the v-t graph for a body in uniform motion.<\/p>\n<figure><center><center><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2019\/11\/velocity-time-graph-uniform-motion.png\" alt=\"velocity time graph uniform motion\" width=\"453\" height=\"318\" \/><\/center><\/center><figcaption><strong>Figure 1 v-t plot for uniform motion<\/strong><\/figcaption><\/figure>\n<p>From this graph, we can see that the v-t graph for uniform motion is a straight line parallel to the time axis.<\/p>\n<h3>Velocity-time graph uniform acceleration<\/h3>\n<p>A body is said to be having uniform acceleration if its velocity changes by an equal amount in equal interval of time. The figure given below shows the v-t plot for a body with uniform acceleration.<\/p>\n<figure><center><center><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2019\/11\/velocity-time-graph-acceleration.png\" alt=\"velocity time graph acceleration\" width=\"445\" height=\"315\" \/><\/center><\/center><figcaption><strong>Figure 2 v-t plot for uniform acceleration<\/strong><\/figcaption><\/figure>\n<h4><strong>Slope of v-t plot<\/strong><\/h4>\n<p>From above plot we can see that \\(AB\\) is the slope of the plot.<br \/>\n\\begin{align*}<br \/>\n\\text{Slop AB}=&amp;\\tan \\theta \\\\<br \/>\n=&amp;\\frac{DE}{CE} = \\frac{v_2-v_1}{t_2t_1}\\\\<br \/>\n=&amp;\\frac{\\text{change in velocity}}{\\text{time interval}} \\\\<br \/>\n=&amp;\\text{ acceleration }(a)<br \/>\n\\end{align*}<br \/>\nHence slope of velocity time graph gives the acceleration of the object.<\/p>\n<h3>Finding displacement from these graphs<\/h3>\n<p>From the velocity-time graph, we can also find the displacement traveled by the particle in a given time interval. The area under the v-t plot gives the distance covered by the body.<br \/>\nConsider the figure given below<\/p>\n<figure><center><center><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2019\/11\/velocity-time-graph-displacement.png\" alt=\"velocity time graph displacement\" width=\"355\" height=\"251\" \/><\/center><\/center><figcaption><strong>Figure 3 v-t plot for displacement<\/strong><\/figcaption><\/figure>\n<p>Here in this figure straight line \\(PQ\\) represents the v-t plot of a body that is moving along a straight-line path and the slope of plot \\(PQ\\) represents the acceleration \\(a\\) of the body.<br \/>\nLet \\(v_0\\) be the initial velocity and \\(v\\) be the velocity at time \\(t\\) respectively.<br \/>\n\\[<br \/>\n\\text{Area under velocity time graph PQ}=\\text{Area of trapezium OPQS}\\\\<br \/>\n=\\text{area under triangle PQR }+\\,\\,\\text{area under rec}\\tan\\text{gle OPRS}\\\\<br \/>\n=\\left( \\frac{1}{2}\\times PR\\times QR \\right) +OP\\times PR\\\\<br \/>\n=PR\\left( \\frac{1}{2}QR+OP \\right) =t\\times \\left( \\frac{1}{2}\\times \\left( v-v_0 \\right) +v_0 \\right)\\\\<br \/>\n=\\frac{1}{2}\\left( v+v_0 \\right) \\times t<br \/>\n=\\text{distance traveled in time }t<br \/>\n\\]<br \/>\nSo, area under trapezium is <em>average velocity times time interval which is equal to displacement of body in time \\(t\\)<\/em><br \/>\nOne point you have to keep in mind is whether the velocity is changing its sign or not.<\/p>\n<ol>\n<li>If velocity is not changing its sign in a particular time interval, then<br \/>\ndisplacement = area under v-t curve.<\/li>\n<li>If velocity is changing its sign, then<br \/>\ndisplacement = area under the v-t curve and distance = sum of the areas of the v-t curve below and above the time axis.<\/li>\n<\/ol>\n<hr \/>\n<h4>Related articles and study material<\/h4>\n<ul>\n<li>learn more about motion graphs by following this link: <a href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/Mechanics\/motgraph.html\"  rel=\"noopener noreferrer\">graphs in motion<\/a><\/li>\n<li>New Simplified Physics by SL Arora Class 11(Set of&#8230; : Book I highly recommend for class 11 students as the language and content is easy to understand.<\/li>\n<li>Mastering Kinematics : Good course on mastering kinematics.<\/li>\n<li>University\u00a0Physics\u00a0with Modern\u00a0Physics: By far my favorite book in physics. This book provides a very good explanation of physics concepts.<\/li>\n<\/ul>\n<hr \/>\n<p><strong>Note to our visitors:-<\/strong><br \/>\nThanks for visiting our website.<br \/>\nDISCLOSURE:\u00a0THIS PAGE MAY CONTAIN AFFILIATE LINKS, MEANING I GET A COMMISSION IF YOU DECIDE TO MAKE A PURCHASE THROUGH MY LINKS, AT NO COST TO YOU. PLEASE READ MY\u00a0DISCLOSURE\u00a0FOR MORE INFO.<\/p>\n<hr \/>\n","protected":false},"excerpt":{"rendered":"<p>Velocity vs Time graph This article is about the velocity-time graph. Before going further details of the topic let us first understand how to draw these graphs. To draw graphs in x-y- plane The independent variable is always taken on the x-axis. We plot the dependent variable on the y-axis. The dependent variable is dependent [&hellip;]<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[14],"tags":[],"class_list":["post-5660","post","type-post","status-publish","format-standard","hentry","category-physics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>What is Velocity time graph? - physicscatalyst&#039;s Blog<\/title>\n<meta name=\"description\" content=\"Velocity-time graph is the graph plotted between velocity of a particle and time. 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Before going further details of the topic let us first understand how to draw these graphs. To draw graphs in x-y- plane The independent variable is always taken on the x-axis. We plot the dependent variable on the y-axis. The dependent variable is dependent&hellip;","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/5660","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/comments?post=5660"}],"version-history":[{"count":3,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/5660\/revisions"}],"predecessor-version":[{"id":6982,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/5660\/revisions\/6982"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=5660"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=5660"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=5660"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}