{"id":3693,"date":"2023-01-09T10:17:03","date_gmt":"2023-01-09T10:17:03","guid":{"rendered":"https:\/\/9thclass.deltapublications.in\/?page_id=3693"},"modified":"2025-04-08T11:12:36","modified_gmt":"2025-04-08T11:12:36","slug":"s-8-e-equations-of-motion-by-graphical-method","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/s-8-e-equations-of-motion-by-graphical-method\/","title":{"rendered":"S-8.e Equations Of Motion By Graphical Method"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Equations Of Motion By Graphical Method<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\"><strong>Key Notes:<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-baad0fc908930daad3e58c25859f5462\" style=\"color:#000060\"><strong>Understanding Graphical Representation<\/strong>:<\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>The equations of motion describe the relationship between displacement, velocity, acceleration, and time.<\/li>\n\n\n\n<li>These relationships can be represented graphically using <strong>velocity-time (v-t)<\/strong> graphs and <strong>displacement-time (s-t)<\/strong> graphs.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9be497d02c5b6f259cde5a03f8f62ec1\" style=\"color:#000060\"><strong>Types of Graphs<\/strong>:<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Velocity-Time (v-t) Graph<\/strong>: Shows how velocity changes with time.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The slope of a velocity-time graph gives <strong>acceleration<\/strong>.<\/li>\n\n\n\n<li>The area under the v-t graph gives <strong>displacement<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Displacement-Time (s-t) Graph<\/strong>: Shows how displacement changes with time.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The slope of a displacement-time graph gives <strong>velocity<\/strong>.<\/li>\n\n\n\n<li>If the graph is a straight line, it indicates uniform motion.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-85196d104b021df290ea0c54375e1459\" style=\"color:#000060\"><strong>Equations of Motion<\/strong>:<\/p>\n\n\n\n<p class=\"has-large-font-size\">The three fundamental equations of motion for uniformly accelerated motion are:<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>v = u + at<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>v<\/strong> = final velocity<\/li>\n\n\n\n<li><strong>u<\/strong> = initial velocity<\/li>\n\n\n\n<li><strong>a<\/strong> = acceleration<\/li>\n\n\n\n<li><strong>t<\/strong> = time<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>s = ut + \u00bdat\u00b2<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>s<\/strong> = displacement<\/li>\n\n\n\n<li><strong>u<\/strong> = initial velocity<\/li>\n\n\n\n<li><strong>a<\/strong> = acceleration<\/li>\n\n\n\n<li><strong>t<\/strong> = time<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>v\u00b2 = u\u00b2 + 2as<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>v<\/strong> = final velocity<\/li>\n\n\n\n<li><strong>u<\/strong> = initial velocity<\/li>\n\n\n\n<li><strong>a<\/strong> = acceleration<\/li>\n\n\n\n<li><strong>s<\/strong> = displacement<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-0fa4d432b267b19062122bb03e123d73\" style=\"color:#000060\"><strong>Graphical Method of Deriving the Equations<\/strong>:<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Velocity-Time Graph<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For <strong>uniform acceleration<\/strong>, the graph is a straight line with a positive or negative slope (depending on the direction of acceleration).<\/li>\n\n\n\n<li>The equation <strong>v = u + at<\/strong> can be derived by observing the slope of the velocity-time graph.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Displacement-Time Graph<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The area under a v-t graph represents displacement, and this can be used to derive <strong>s = ut + \u00bdat\u00b2<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Slope and Area Interpretation<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The slope of the displacement-time graph gives the instantaneous velocity.<\/li>\n\n\n\n<li>The area under the velocity-time graph gives the total displacement.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-c8f44e10c70daf0d83acddd1b14923d7\" style=\"color:#000060\"><strong>Derivation of Equations Using Graphs<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>First Equation<\/strong>: From a v-t graph, the slope represents acceleration, so <strong>a = (v &#8211; u)\/t<\/strong>. Rearranging gives <strong>v = u + at<\/strong>.<\/li>\n\n\n\n<li><strong>Second Equation<\/strong>: From the area under the v-t graph, the displacement is given by the area of the trapezoid, which simplifies to <strong>s = ut + \u00bdat\u00b2<\/strong>.<\/li>\n\n\n\n<li><strong>Third Equation<\/strong>: By considering the kinematic relations and the area under the velocity-time graph, we can derive <strong>v\u00b2 = u\u00b2 + 2as<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-5f674220bcbb6fb2fef6c40b6c208737\" style=\"color:#000060\"><strong>Applications<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>These equations are used to solve problems related to motion in a straight line, like calculating final velocity, displacement, and time when acceleration is constant.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-c04aed99344ccef2da12b0b1b0f37282\" style=\"color:#000060\"><strong>Example Problems<\/strong>:<\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Calculate the displacement of a body given its velocity-time graph.<\/li>\n\n\n\n<li>Use the graphical method to find the acceleration from a velocity-time graph.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color\" style=\"color:#d90000\">Let&#8217;s practice!<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/82461\/200\/941\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-2-36.png\" alt=\"\" class=\"wp-image-6447\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-2-36.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-2-36-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-2-36-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/81561\/239\/928\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-1-1-38.png\" alt=\"\" class=\"wp-image-6448\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-1-1-38.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-1-1-38-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/03\/Worksheet-1-1-1-38-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Equations Of Motion By Graphical Method Key Notes: Understanding Graphical Representation: Types of Graphs: Velocity-Time (v-t) Graph: Shows how velocity changes with time. Displacement-Time (s-t) Graph: Shows how displacement changes with time. Equations of Motion: The three fundamental equations of motion for uniformly accelerated motion are: v = u + at s = ut +<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/s-8-e-equations-of-motion-by-graphical-method\/\">Continue reading <span class=\"screen-reader-text\">&#8220;S-8.e Equations Of Motion By Graphical Method&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-3693","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/3693","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=3693"}],"version-history":[{"count":17,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/3693\/revisions"}],"predecessor-version":[{"id":16677,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/3693\/revisions\/16677"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=3693"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}