{"id":1154,"date":"2024-08-17T11:42:36","date_gmt":"2024-08-17T11:42:36","guid":{"rendered":"https:\/\/www.meniit.com\/study-material\/?p=1154"},"modified":"2024-08-17T11:43:28","modified_gmt":"2024-08-17T11:43:28","slug":"motion-straight-line","status":"publish","type":"post","link":"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line","title":{"rendered":"Motion in a Straight Line"},"content":{"rendered":"<h2>REST AND MOTION<\/h2>\n<p style=\"text-align: justify;\">An object is said to be in motion with respect to an observer, if its position changes w.r.t. that observer. It may happen by both ways either observer moves or object moves.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1155 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/rest-motion.png\" alt=\"rest motion\" width=\"704\" height=\"224\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/rest-motion.png 704w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/rest-motion-300x95.png 300w\" sizes=\"auto, (max-width: 704px) 100vw, 704px\" \/><\/p>\n<ul>\n<li>Boy B is in motion w.r.t. ground but boy B is at rest w.r.t. moving car,<\/li>\n<li>Boy A is at rest w.r.t. ground but boy A is in motion w.r.t. boy B or moving car.<\/li>\n<\/ul>\n<p>Position, Distance and Displacement<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1157 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/diagram-15.png\" alt=\"diagram\" width=\"266\" height=\"205\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Position:<\/strong> Location of an object at any instant of time is known as its position with respect to a reference point.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1156 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-22.png\" alt=\"formula\" width=\"295\" height=\"39\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Distance:<\/strong> Actual length of the path travelled by an object in a given interval of time is known as distance travelled. Distance is defined in terms of magnitude only; no direction is associated with distance. So it\u2019s a Scalar quantity.<\/p>\n<p style=\"text-align: justify;\">Actual length of path = \u03c0R<\/p>\n<p style=\"text-align: justify;\"><strong>Displacement:<\/strong> Shortest distance between the initial and final position of the particle in a particular direction is known as displacement. Displacement is defined with magnitude as well as direction. So it\u2019s a Vector quantity.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1160 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/formula-23.png\" alt=\"formula\" width=\"119\" height=\"34\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1161 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/diagram-16.png\" alt=\"diagram\" width=\"244\" height=\"165\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/diagram-16.png 244w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/diagram-16-95x65.png 95w\" sizes=\"auto, (max-width: 244px) 100vw, 244px\" \/><\/p>\n<p style=\"text-align: justify;\">The subscripts i and f refer to the initial and final positions. These are not necessarily the positions from which the particle starts its motion nor where its motion ceases. The i and f designate the particular initial and final positions we are considering out of the entire motion of the object<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1162 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/displacement.png\" alt=\"displacement\" width=\"324\" height=\"59\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/displacement.png 324w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/displacement-300x55.png 300w\" sizes=\"auto, (max-width: 324px) 100vw, 324px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1163 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/07\/displacement-diagram.png\" alt=\"displacement diagram\" width=\"251\" height=\"191\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>| Displacement | \u2264 Distance :<\/strong> Magnitude of displacement is always less than or equals to distance travelled. For a particle moving in a straight line without changing its direction magnitude of displacement and distance becomes equal.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_69_1 counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#Average-and-Instantaneous-Velocity\" title=\"Average and Instantaneous Velocity\">Average and Instantaneous Velocity<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#Average-and-Instantaneous-Speed\" title=\"Average and Instantaneous Speed\">Average and Instantaneous Speed<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#Cases-of-Average-Speed\" title=\"Cases of Average Speed\">Cases of Average Speed<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#Average-and-Instantaneous-Acceleration\" title=\"Average and Instantaneous Acceleration\">Average and Instantaneous Acceleration<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#Kinematics-Equations-For-Uniformly-Accelerated-Motion\" title=\"Kinematics Equations For Uniformly Accelerated Motion\">Kinematics Equations For Uniformly Accelerated Motion<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#Sign-Conventions-for-Vectors-in-Straight-Line-Motion\" title=\"Sign Conventions for Vectors in Straight Line Motion\">Sign Conventions for Vectors in Straight Line Motion<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#Difference-between-Acceleration-and-Retardation\" title=\"Difference between Acceleration and Retardation\">Difference between Acceleration and Retardation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#Motion-Under-Gravity\" title=\"Motion Under Gravity\">Motion Under Gravity<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#GRAPHS\" title=\"GRAPHS\">GRAPHS<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#RELATIVE-VELOCITY\" title=\"RELATIVE VELOCITY\">RELATIVE VELOCITY<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\/#RELATIVE-VELOCITY-2\" title=\"RELATIVE VELOCITY\">RELATIVE VELOCITY<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Average-and-Instantaneous-Velocity\"><\/span>Average and Instantaneous Velocity<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Average Velocity:<\/strong> Change in position of a particle w.r.t. a finite interval of time is known as average velocity of that interval.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1241 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/average-velocity-1.png\" alt=\"average velocity\" width=\"227\" height=\"244\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1239 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/average-velocity.png\" alt=\"average velocity\" width=\"267\" height=\"62\" \/><\/p>\n<p style=\"text-align: justify;\">Slope of secant of displacement vs. time graph gives average velocity.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1240 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula.png\" alt=\"formula\" width=\"182\" height=\"61\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Instantaneous Velocity :<\/strong> Change in position of a particle w.r.t. an infinitesimally small interval of time is known as instantaneous velocity of that instant.<br \/>\nLimit of average velocity as the \u2206t becomes infinitesimally small is known as instantaneous velocity.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1245 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/Instantaneous-velocity.png\" alt=\"Instantaneous velocity\" width=\"259\" height=\"207\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1242 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-1.png\" alt=\"formula\" width=\"303\" height=\"69\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-1.png 303w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-1-300x68.png 300w\" sizes=\"auto, (max-width: 303px) 100vw, 303px\" \/><\/p>\n<p style=\"text-align: justify;\">Infinitesimally small means it approaches to zero. When limit approaches to zero than it converts into derivative of r w.r.t. t<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1243 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-2.png\" alt=\"formula\" width=\"165\" height=\"59\" \/><\/p>\n<p style=\"text-align: justify;\">Slope of tangent of displacement vs time graph gives instantaneous velocity.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1244 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-3.png\" alt=\"formula \" width=\"180\" height=\"72\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Average-and-Instantaneous-Speed\"><\/span>Average and Instantaneous Speed<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Average speed<\/strong> is defined as total distance travelled by a particle divided by the total time taken.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1246 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/average-speed.png\" alt=\"average speed \" width=\"352\" height=\"56\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/average-speed.png 352w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/average-speed-300x48.png 300w\" sizes=\"auto, (max-width: 352px) 100vw, 352px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Instantaneous speed<\/strong> is equals to the magnitude of Instantaneous velocity.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1247 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-4.png\" alt=\"formula\" width=\"187\" height=\"64\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Cases-of-Average-Speed\"><\/span>Cases of Average Speed<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Let initial speed of an object is v 1, final speed is v2 and <strong>acceleration is constant<\/strong>, then<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1248 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-5.png\" alt=\"formula\" width=\"151\" height=\"53\" \/><\/p>\n<ul>\n<li style=\"text-align: justify;\">A body covers a distance s<sub>1<\/sub> in time t<sub>1<\/sub>, s<sub>2<\/sub> in time t<sub>2<\/sub> and s<sub>3<\/sub> in time t<sub>3<\/sub>.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1249 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-6.png\" alt=\"formula\" width=\"193\" height=\"59\" \/><\/p>\n<ul>\n<li style=\"text-align: justify;\">A body travels with speed v<sub>1<\/sub> for a time t<sub>1<\/sub>, v<sub>2<\/sub> for time t<sub>2<\/sub> and v<sub>3<\/sub> for the time t<sub>3<\/sub>.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1250 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-7.png\" alt=\"formula\" width=\"231\" height=\"64\" \/><\/p>\n<ul>\n<li style=\"text-align: justify;\">A body covers a distance s<sub>1<\/sub> with speed v<sub>1<\/sub>, s<sub>2<\/sub> with speed v<sub>2<\/sub> and s<sub>3<\/sub> with speed v<sub>3<\/sub>.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1251 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-8.png\" alt=\"formula\" width=\"191\" height=\"84\" \/><\/p>\n<p>A boy goes from home to school with speed v<sub>1<\/sub> and come back to home with speed v<sub>2<\/sub>.<br \/>\nHere distance covered by the boy is same. Time taken by the boy from home to school<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1252 aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-9.png\" alt=\"formula\" width=\"94\" height=\"57\" \/><\/p>\n<p style=\"text-align: justify;\">and time taken by the boy from school to home<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1253 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-10.png\" alt=\"formula\" width=\"413\" height=\"132\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-10.png 413w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-10-300x96.png 300w\" sizes=\"auto, (max-width: 413px) 100vw, 413px\" \/><\/p>\n<p style=\"text-align: justify;\">If an object covered one third distance with speed u, next one third with speed v and last one third distance with speed w then,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1254 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-11.png\" alt=\"formula\" width=\"184\" height=\"56\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Average-and-Instantaneous-Acceleration\"><\/span>Average and Instantaneous Acceleration<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Average acceleration:<\/strong> Rate of change of velocity w.r.t. a time interval is known as average acceleration.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1255 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-12.png\" alt=\"formula\" width=\"368\" height=\"128\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-12.png 368w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-12-300x104.png 300w\" sizes=\"auto, (max-width: 368px) 100vw, 368px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Instantaneous acceleration:<\/strong> Acceleration at a particular instant of time during its motion is known as instantaneous acceleration, it is given as the limit of average acceleration at any time interval \u2206t approaches to zero.<\/p>\n<p style=\"text-align: justify;\">Derivative of velocity w.r.t. time is known as instantaneous acceleration.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1256 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-13.png\" alt=\"formula\" width=\"474\" height=\"109\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-13.png 474w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-13-300x69.png 300w\" sizes=\"auto, (max-width: 474px) 100vw, 474px\" \/><\/p>\n<h2>KINEMATICS<\/h2>\n<h3><span class=\"ez-toc-section\" id=\"Kinematics-Equations-For-Uniformly-Accelerated-Motion\"><\/span>Kinematics Equations For Uniformly Accelerated Motion<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">If a particle is accelerated with constant acceleration for an interval of time, then the motion is termed as uniformly accelerated motion in that interval of time.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1257 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/kinematics.png\" alt=\"kinematics\" width=\"761\" height=\"129\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/kinematics.png 761w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/kinematics-300x51.png 300w\" sizes=\"auto, (max-width: 761px) 100vw, 761px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Sign-Conventions-for-Vectors-in-Straight-Line-Motion\"><\/span>Sign Conventions for Vectors in Straight Line Motion<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Since the motion is on straight line, each vector has two possible directions at a particular time instant. You can choose any one direction as positive and the opposite direction as negative.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1258 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/line-of-motion.png\" alt=\"line of motion\" width=\"313\" height=\"279\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/line-of-motion.png 313w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/line-of-motion-300x267.png 300w\" sizes=\"auto, (max-width: 313px) 100vw, 313px\" \/><\/p>\n<p><strong>For example :<\/strong><\/p>\n<ol>\n<li style=\"text-align: justify;\">A particle is moving in horizontal direction (say along x-axis). If the vectors directed towards right are taken as positive then the vectors directed towards left are taken as negative.<\/li>\n<li style=\"text-align: justify;\">Similarly, for a particle moving in vertical direction, (say along y-axis) the vectors directed upward may be taken as positive and thus, those directed downwards will be negative.<\/li>\n<li style=\"text-align: justify;\">For motion along inclined plane or any other arbitrary direction, if the vectors directed up the plane are positive, then the vectors directed down the plane are negative. You can take any direction of motion as +ve direction and the direction opposite to that becomes negative direction.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Difference-between-Acceleration-and-Retardation\"><\/span>Difference between Acceleration and Retardation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">When the speed of a particle decreases or when the particle slows down, the motion is said to be under deceleration or retardation. The necessary requirement for retardation is that the velocity (v) and acceleration (a) should be opposite in direction.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1259 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-14.png\" alt=\"formula\" width=\"679\" height=\"297\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-14.png 679w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-14-300x131.png 300w\" sizes=\"auto, (max-width: 679px) 100vw, 679px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Motion-Under-Gravity\"><\/span>Motion Under Gravity<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Suppose a particle is thrown with speed u (vertically upward)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1260 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-15.png\" alt=\"formula\" width=\"532\" height=\"189\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-15.png 532w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-15-300x107.png 300w\" sizes=\"auto, (max-width: 532px) 100vw, 532px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1261 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram.png\" alt=\"diagram\" width=\"224\" height=\"254\" \/><\/p>\n<p style=\"text-align: justify;\">The above results can be easily calculated by equations of motion.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"GRAPHS\"><\/span><strong>GRAPHS<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Position (x) vs Time (t) graph<\/strong><\/p>\n<ul>\n<li><strong>Average Velocity:<\/strong><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1262 size-full aligncenter\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/average-velocity-2.png\" alt=\"average velocity\" width=\"425\" height=\"333\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/average-velocity-2.png 425w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/average-velocity-2-300x235.png 300w\" sizes=\"auto, (max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li><strong>Instantaneous Velocity :<\/strong><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1263 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/Instantaneous-velocity-1.png\" alt=\"Instantaneous velocity\" width=\"418\" height=\"318\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/Instantaneous-velocity-1.png 418w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/Instantaneous-velocity-1-300x228.png 300w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><\/p>\n<p><strong>Velocity (v) vs Time (t) graph<\/strong><\/p>\n<ul>\n<li><strong>Average Acceleration :<\/strong><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1264 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram-1.png\" alt=\"diagram\" width=\"379\" height=\"348\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram-1.png 379w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram-1-300x275.png 300w\" sizes=\"auto, (max-width: 379px) 100vw, 379px\" \/><\/p>\n<ul>\n<li><strong>Instantaneous Acceleration :<\/strong><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1265 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram-2.png\" alt=\"diagram\" width=\"368\" height=\"236\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram-2.png 368w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram-2-300x192.png 300w\" sizes=\"auto, (max-width: 368px) 100vw, 368px\" \/><\/p>\n<p><strong>Velocity (v) vs Time (t) graph<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1267 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/displacement-path.png\" alt=\"displacement path\" width=\"680\" height=\"285\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/displacement-path.png 680w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/displacement-path-300x126.png 300w\" sizes=\"auto, (max-width: 680px) 100vw, 680px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"RELATIVE-VELOCITY\"><\/span>RELATIVE VELOCITY<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Velocity, position, acceleration all are frame dependent quantities. All of them can be calculated with respect to a frame or reference point<\/p>\n<h3><span class=\"ez-toc-section\" id=\"RELATIVE-VELOCITY-2\"><\/span>RELATIVE VELOCITY<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">Velocity, position, acceleration all are frame dependent quantities. All of them can be calculated with respect to a frame or reference point<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1268 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-16.png\" alt=\"formula\" width=\"467\" height=\"201\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-16.png 467w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-16-300x129.png 300w\" sizes=\"auto, (max-width: 467px) 100vw, 467px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1269 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/fixed-point.jpg\" alt=\"fixed point\" width=\"320\" height=\"160\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/fixed-point.jpg 320w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/fixed-point-300x150.jpg 300w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/p>\n<p style=\"text-align: justify;\">So with the above discussion we concluded that, if A and B are moving along the same direction then,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1270 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/formula-17.png\" alt=\"formula\" width=\"252\" height=\"31\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1271 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram-3.png\" alt=\"diagram\" width=\"182\" height=\"108\" \/><\/p>\n<p style=\"text-align: justify;\">If A and B are moving in opposite directions<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1272 size-full\" src=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram-4.png\" alt=\"diagram\" width=\"363\" height=\"157\" srcset=\"https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram-4.png 363w, https:\/\/www.meniit.com\/study-material\/wp-content\/uploads\/2024\/08\/diagram-4-300x130.png 300w\" sizes=\"auto, (max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<div class=\"newspaper-x-tags\"><strong>TAGS: <\/strong><span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/average-and-instantaneous-acceleration\" rel=\"tag\">Average and Instantaneous Acceleration<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/average-and-instantaneous-speed\" rel=\"tag\">Average and Instantaneous Speed<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/average-and-instantaneous-velocity\" rel=\"tag\">Average and Instantaneous Velocity<\/a><\/span><a href=\"https:\/\/www.meniit.com\/study-material\/tag\/motion-in-a-straight-line\" rel=\"tag\">Motion in a Straight Line<\/a> <\/div>\n","protected":false},"excerpt":{"rendered":"<p>REST AND MOTION An object is said to be in motion with respect to an observer, if its position changes&nbsp;&nbsp;&#8230;.<a class=\"read_more\" href=\"https:\/\/www.meniit.com\/study-material\/neet\/class-11th\/physics-class-11th\/motion-straight-line\" rel=\"nofollow\">Read More >><\/a><\/p>\n","protected":false},"author":5,"featured_media":1281,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"om_disable_all_campaigns":false,"rank_math_lock_modified_date":false,"footnotes":""},"categories":[425,241,240],"tags":[434,433,432,431],"class_list":["post-1154","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-physics-class-11th","category-class-11th","category-neet","tag-average-and-instantaneous-acceleration","tag-average-and-instantaneous-speed","tag-average-and-instantaneous-velocity","tag-motion-in-a-straight-line"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/1154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/comments?post=1154"}],"version-history":[{"count":6,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/1154\/revisions"}],"predecessor-version":[{"id":1282,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/posts\/1154\/revisions\/1282"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/media\/1281"}],"wp:attachment":[{"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/media?parent=1154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/categories?post=1154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.meniit.com\/study-material\/wp-json\/wp\/v2\/tags?post=1154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}