{"id":7347,"date":"2022-09-06T03:48:40","date_gmt":"2022-09-05T22:18:40","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=7347"},"modified":"2022-11-17T15:21:45","modified_gmt":"2022-11-17T09:51:45","slug":"motion-in-a-straight-line-formulas","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/motion-in-a-straight-line-formulas\/","title":{"rendered":"Motion in a straight line formulas"},"content":{"rendered":"\n<p>On this page find all the formulas you need to remember for motion in a straight line. These are the important formulas if you are in class 11 or preparing for NEET, JEE-Mains or JEE-Advanced.<br>I will attach a downloadable PDF file of this article so that you can print it out for your preparation and studies. We also have topic-wise notes on <a href=\"https:\/\/physicscatalyst.com\/class11.php\">class 11 physics<\/a> where you can have notes, worksheets etc for free.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Motion in a straight line class 11 formulas<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Distance &#8211;<\/strong> The total length that is travelled between different positions.<\/li>\n\n\n\n<li><strong>Displacement &#8211;<\/strong> Distance between two points in a particular direction.\n<ul class=\"wp-block-list\">\n<li>Formula :- $\\Delta x= x_f-x_i$<\/li>\n\n\n\n<li>$\\Delta x \\rightarrow$ Displacement<\/li>\n\n\n\n<li>$x_f\\rightarrow$ final position<\/li>\n\n\n\n<li>$x_i\\rightarrow$ initial position<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Speed &#8211;<\/strong> the total distance covered divided by the time taken to cover that distance.\n<ul class=\"wp-block-list\">\n<li>Formula :- $\\text{Speed}=\\frac{\\text{Total Distance Covered}}{\\text{Time Taken}}$<\/li>\n\n\n\n<li>Unit &#8211; $m\/s$, $Km\/hr$ or $mph$(mile per hour)<\/li>\n\n\n\n<li>Dimensions &#8211; $[M^0LT^{-1}]$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Velocity &#8211;<\/strong> the displacement divided by the time it takes for the displacement\n<ul class=\"wp-block-list\">\n<li>Formula :- $Velocity=\\frac{Displacement}{Time}$<\/li>\n\n\n\n<li>Unit &#8211; $m\/s$, $Km\/hr$ or $mph$(mile per hour)<\/li>\n\n\n\n<li>Dimensions &#8211; $[M^0LT^{-1}]$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Average Speed &#8211;<\/strong> the total distance covered divided by the time taken to cover that distance\n<ul class=\"wp-block-list\">\n<li>Formula :- $\\text{Average Speed}=\\frac{\\text{Total Distance Covered}}{\\text{Time Taken}}=\\frac{\\Delta x}{\\Delta t}$<\/li>\n\n\n\n<li>Body covering different distances with different speeds $$\\bar v=\\frac{s_1+s_2+s_3+\u2026.}{t_1+t_2+t_3+\u2026.}=\\frac{s_1+s_2+s_3+\u2026.}{\\frac{s_1}{v_1}+\\frac{s_2}{v_2}+\\frac{s_3}{v_3}+\u2026..}$$<\/li>\n\n\n\n<li>If the body covers the first half of the total distance with speed $v_1$ and the second half with the speed $v_2$, then the average speed is given by $$\\bar v=\\frac{2v_1v_2}{v_1+v_2}$$<br>In this case, the average speed is the harmonic mean of individual speeds.<\/li>\n\n\n\n<li>The body is moving at different speeds in different time intervals and then <br>Total distance travelled $=v_1t_1+v_2t_2+v_3t_3+\u2026.$ <br>Total time taken $=t_1+t_2+t_3+\u2026.$ <br>$$\\bar v= \\frac{v_1t_1+v_2t_2+v_3t_3+\u2026.}{t_1+t_2+t_3+\u2026.}$$\n<ul class=\"wp-block-list\">\n<li>If $t_1=t_2=t_3=\u2026.=t_n=t$ then, <br>$$\\bar v=\\frac{(v_1+v_2+v_3+\u2026.)t}{nt}=\\frac{(v_1+v_2+v_3+\u2026.)}{n}$$\n<ul class=\"wp-block-list\">\n<li>In this case, the average speed is the arithmetic mean of the individual speeds.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Average Velocity &#8211;<\/strong> the total displacement covered divided by the time taken for that displacement\n<ul class=\"wp-block-list\">\n<li>Formula :- $\\text{Average Velocity}=\\frac{\\text{Displacement}}{\\text{Time Taken}} \\,\\,\\,\\,\\,\\,or,\\,\\,\\,\\,\\, \\bar v=\\frac{\\Delta \\vec x}{\\Delta t}$<\/li>\n\n\n\n<li>Finding position from velocity &#8211; $x = x_{0} + \\bar{v} t$<\/li>\n\n\n\n<li>Learn more on the <a href=\"https:\/\/physicscatalyst.com\/mech\/Speed-and-Velocity.php\">average speed and velocity<\/a> page.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Instantaneous Velocity &#8211;<\/strong> is defined as the velocity of an object at a particular instant of time.\n<ul class=\"wp-block-list\">\n<li>Formula :- $v(t) = \\frac{dx(t)}{dt}$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Instantaneous Speed &#8211;<\/strong> is defined as the speed of an object at a particular instant of time. It is the absolute value of instantaneous velocity.\n<ul class=\"wp-block-list\">\n<li>Formula :- $\\text{Instantaneous speed} = |v(t)|$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Acceleration &#8211;<\/strong> The rate of change of velocity is called acceleration.\n<ul class=\"wp-block-list\">\n<li>Formula :- $a=\\frac{\\Delta \\vec{v}}{\\Delta t}=\\frac{v_f-v_i}{t_f-t_i}$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Instantaneous acceleration &#8211;<\/strong> acceleration of a particle at a particular instant of time\n<ul class=\"wp-block-list\">\n<li>Formula :- $a=\\lim_{\\Delta\\rightarrow0}\\frac{\\Delta v}{\\Delta t}=\\frac{dv}{dt}$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Equations of motion with constant acceleration<\/strong>\n<ul class=\"wp-block-list\">\n<li>First Equation of motion &#8211; finding velocity from acceleration &#8211; $v=v_0+at$<\/li>\n\n\n\n<li>Second Equation of motion &#8211; finding position from velocity and acceleration &#8211; $x = x_{0} + v_{0} t + \\frac{1}{2} at^{2}$<\/li>\n\n\n\n<li>Third Equation of motion &#8211; finding velocity from distance and acceleration &#8211; $v^{2} = v_{0}^{2} + 2a(x &#8211; x_{0})$<\/li>\n\n\n\n<li>Equation for finding distance travelled in $n^{th}$ second of object&#8217;s journey &#8211; $S_n=u+a(n-\\frac{1}{2})$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Motion under gravity<\/strong>\n<ul class=\"wp-block-list\">\n<li>Equations of motion for a freely falling body\n<ul class=\"wp-block-list\">\n<li>$v=u+gt$<\/li>\n\n\n\n<li>$s=ut+\\frac{1}{2}gt^2$<\/li>\n\n\n\n<li>$v^2-u^2=2gs$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>For a body falling freely under the action of gravity, $g$ is taken as positive.<\/li>\n\n\n\n<li>For the body thrown vertically upwards, $g$ is taken as negative.<\/li>\n\n\n\n<li>When the body is just dropped, $u=0$<\/li>\n\n\n\n<li>For a body thrown vertically up with initial velocity $u$<\/li>\n\n\n\n<li>Maximum height reached is, $h=\\frac{u^2}{2g}$<\/li>\n\n\n\n<li>time of ascent = time of descent $=\\frac{u}{g}$<\/li>\n\n\n\n<li>total time of flight $=\\frac{2u}{g}$<\/li>\n\n\n\n<li>the velocity of fall at the point of projection $=u$<\/li>\n\n\n\n<li>velocity attained by a body dropped from height $h$, $v=\\sqrt{2gh}$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Relative Velocity<\/strong>\n<ul class=\"wp-block-list\">\n<li>Relative velocity of object $A$ w.r.t. object $B$ is, $v_{AB}=v_A-v_B$<\/li>\n\n\n\n<li>When two objects are moving in the same direction, $v_{AB}=v_A-v_B$<\/li>\n\n\n\n<li>When two objects are moving in opposite directions, $v_{AB}=v_A+v_B$<\/li>\n\n\n\n<li>When $v_A$ and $V_B$&nbsp;are inclined to each other at an angle&nbsp;$\\theta$ $$\\vec{v}_{AB}=\\sqrt{v_A^2+v_B^2-2v_Av_B\\cos\\theta}$$<\/li>\n\n\n\n<li>If $v_{AB}$ makes an angle $\\beta$ with $v_A$, then $$\\tan\\beta=\\frac{v_B\\sin\\theta}{v_A-v_B\\cos\\theta}$$<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Rectilinear Motion Formula PDF File Download<\/h2>\n\n\n\n<p>Download this free <a href=\"https:\/\/physicscatalyst.com\/article\/motion-in-a-straight-line\/\">Motion in a straight line<\/a> formula for neet, class 11 and jee as a pdf. Learn more about what is <a href=\"https:\/\/physicscatalyst.com\/article\/rectilinear-motion\/\">Rectilinear Motion<\/a> in physics. <\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2022\/09\/motion-in-a-straight-line-formulas.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 1D-Kinematics-formula-list.\"><\/object><a id=\"wp-block-file--media-7882967b-446a-4fa8-9a16-b921a1065002\" href=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2022\/09\/motion-in-a-straight-line-formulas.pdf\">1D-Kinematics-formula-list<\/a><a href=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2022\/09\/motion-in-a-straight-line-formulas.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-7882967b-446a-4fa8-9a16-b921a1065002\">Download<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>On this page find all the formulas you need to remember for motion in a straight line. These are the important formulas if you are in class 11 or preparing for NEET, JEE-Mains or JEE-Advanced.I will attach a downloadable PDF file of this article so that you can print it out for your preparation and [&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-7347","post","type-post","status-publish","format-standard","hentry","category-physics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Motion in a straight line formulas for NEET, JEE and Class 11<\/title>\n<meta name=\"description\" content=\"Get Motion in straight line formulas, for class 11, NEET and JEE at physicscatalyst.com. 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These are the important formulas if you are in class 11 or preparing for NEET, JEE-Mains or JEE-Advanced.I will attach a downloadable PDF file of this article so that you can print it out for your preparation and&hellip;","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7347","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=7347"}],"version-history":[{"count":9,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7347\/revisions"}],"predecessor-version":[{"id":7562,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/7347\/revisions\/7562"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=7347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=7347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=7347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}