{"id":6775,"date":"2026-04-02T05:19:48","date_gmt":"2026-04-01T23:49:48","guid":{"rendered":"https:\/\/enlightify.org\/?p=6775"},"modified":"2026-06-13T17:42:33","modified_gmt":"2026-06-13T12:12:33","slug":"equations-of-motion-under-gravity","status":"publish","type":"post","link":"https:\/\/enlightify.org\/hi\/equations-of-motion-under-gravity\/","title":{"rendered":"Equations of Motion Under Gravity"},"content":{"rendered":"\t\t
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Equations of Motion Under Gravity<\/h1>\n\n

Introduction<\/h2>\n

\nWhen an object moves under the influence of gravity alone, its motion is called motion under gravity. In such motion, the acceleration is constant and is equal to the acceleration due to gravity (g).\n<\/p>\n\n

\nThese motions are explained using the standard equations of motion by replacing acceleration (a) with g.\n<\/p>\n\n

Definition<\/h2>\n

\nEquations of motion under gravity are the mathematical relations that describe the motion of a body when it is moving vertically under the influence of gravitational force.\n<\/p>\n\n

Explanation<\/h2>\n

\nNear the surface of the Earth, every freely falling body experiences a constant acceleration called acceleration due to gravity (g \u2248 9.8 m\/s\u00b2).\n<\/p>\n\n

\nBy replacing acceleration (a) with g in the equations of motion, we get:\n<\/p>\n\n

\nv = u + gt\n<\/p>\n\n

\ns = ut + (1\/2)gt\u00b2\n<\/p>\n\n

\nv\u00b2 = u\u00b2 + 2gs\n<\/p>\n\n

\nWhere:\n<\/p>\n

    \n
  • u = initial velocity<\/li>\n
  • v = final velocity<\/li>\n
  • s = displacement<\/li>\n
  • t = time<\/li>\n
  • g = acceleration due to gravity<\/li>\n<\/ul>\n\n

    Sign Convention<\/h2>\n

    \nThe direction of motion is very important while solving problems:\n<\/p>\n\n

      \n
    • If the body is moving downward (free fall), g is taken as positive.<\/li>\n
    • If the body is thrown upward, g is taken as negative.<\/li>\n<\/ul>\n\n

      \nIn simple terms:\n<\/p>\n\n

        \n
      • Upward motion \u2192 velocity decreases \u2192 g is negative<\/li>\n
      • Downward motion \u2192 velocity increases \u2192 g is positive<\/li>\n<\/ul>\n\n

        Types<\/h2>\n\n

        1. Body Falling Downward<\/h3>\n
          \n
        • Initial velocity (u) = 0 (if dropped)<\/li>\n
        • g is positive<\/li>\n
        • Velocity increases with time<\/li>\n<\/ul>\n\n

          2. Body Thrown Upward<\/h3>\n
            \n
          • Initial velocity (u) is upward<\/li>\n
          • g is negative<\/li>\n
          • Velocity decreases until it becomes zero at highest point<\/li>\n<\/ul>\n\n

            3. Highest Point<\/h3>\n
              \n
            • Final velocity (v) = 0<\/li>\n
            • Acceleration is still g downward<\/li>\n<\/ul>\n\n

              Importance<\/h2>\n
                \n
              • Used to calculate height, time, and velocity of falling objects<\/li>\n
              • Helps in understanding motion of projectiles<\/li>\n
              • Important in solving numerical problems in physics<\/li>\n<\/ul>\n\n

                Examples<\/h2>\n
                  \n
                • A stone falling from a building<\/li>\n
                • A ball thrown upward and coming back down<\/li>\n
                • Rain falling from clouds<\/li>\n<\/ul>\n\n

                  \nAn important point:\n<\/p>\n\n

                    \n
                  • All bodies fall with the same acceleration (g) regardless of their mass (ignoring air resistance)<\/li>\n<\/ul>\n\n

                    Important Points<\/h2>\n
                      \n
                    • Acceleration due to gravity (g) is constant near Earth surface<\/li>\n
                    • For downward motion, g is taken as positive<\/li>\n
                    • For upward motion, g is taken as negative<\/li>\n
                    • At highest point, velocity becomes zero<\/li>\n
                    • Time of ascent equals time of descent (for same height)<\/li>\n
                    • All bodies fall with same acceleration (independent of mass)<\/li>\n
                    • Choose correct equation based on known values<\/li>\n<\/ul>\n\n

                      Conclusion<\/h2>\n

                      \nEquations of motion under gravity help us understand and calculate the motion of objects moving vertically under Earth's gravitational force. By applying proper sign conventions and formulas, we can easily solve various real-life and numerical problems.\n<\/p>\n\n

                      \nStructure inspired from gravitational concepts explanation :contentReference[oaicite:0]{index=0}\n<\/p>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

                      Equations of Motion Under Gravity Introduction When an object moves under the influence of gravity alone, its motion is called motion under gravity. In such motion, the acceleration is constant and is equal to the acceleration due to gravity (g). These motions are explained using the standard equations of motion by replacing acceleration (a) with […]<\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"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":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","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":"set","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":[98],"tags":[],"class_list":["post-6775","post","type-post","status-publish","format-standard","hentry","category-physics"],"_links":{"self":[{"href":"https:\/\/enlightify.org\/hi\/wp-json\/wp\/v2\/posts\/6775","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/enlightify.org\/hi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/enlightify.org\/hi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/enlightify.org\/hi\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/enlightify.org\/hi\/wp-json\/wp\/v2\/comments?post=6775"}],"version-history":[{"count":1,"href":"https:\/\/enlightify.org\/hi\/wp-json\/wp\/v2\/posts\/6775\/revisions"}],"predecessor-version":[{"id":7580,"href":"https:\/\/enlightify.org\/hi\/wp-json\/wp\/v2\/posts\/6775\/revisions\/7580"}],"wp:attachment":[{"href":"https:\/\/enlightify.org\/hi\/wp-json\/wp\/v2\/media?parent=6775"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/enlightify.org\/hi\/wp-json\/wp\/v2\/categories?post=6775"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/enlightify.org\/hi\/wp-json\/wp\/v2\/tags?post=6775"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}