{"id":254234,"date":"2022-09-10T11:13:43","date_gmt":"2022-09-10T05:43:43","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-particle-projected-with-velocity-v0-along-x-axis-the-deceleration-on-the-particle-is-proportional-to-the-square-of-the-distance-from-the-origin-i-e-a%e2%88%92%ce%b1x2-the-distance-at-wh\/"},"modified":"2022-09-10T11:13:43","modified_gmt":"2022-09-10T05:43:43","slug":"a-particle-projected-with-velocity-v0-along-x-axis-the-deceleration-on-the-particle-is-proportional-to-the-square-of-the-distance-from-the-origin-i-e-a%e2%88%92%ce%b1x2-the-distance-at-wh","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/","title":{"rendered":"A particle projected with velocity V0     along x-axis. The deceleration on the particle is  proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2     . The distance at which the particle stops is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A particle projected with velocity V0 along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2 . The distance at which the particle stops is","custom_permalink":"question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/"},"categories":[],"acf":{"question":"<p>A particle projected with velocity <math><mrow><msub><mi>V<\/mi><mn>0<\/mn><\/msub><\/mrow><\/math><xml>     <\/xml>along x-axis. The deceleration on the particle is  proportional to the square of the distance from the origin i.e <math><mrow><mi>a<\/mi><mo>=<\/mo><mo>\u2212<\/mo><mi>\u03b1<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mrow><\/math><xml>     <\/xml>. The distance at which the particle stops is<\/p>","options":[{"option":"<p>    <math><mrow><msqrt><mrow><mfrac><mrow><mn>3<\/mn><msub><mi>V<\/mi><mn>0<\/mn><\/msub><\/mrow><mrow><mn>2<\/mn><mi>\u03b1<\/mi><\/mrow><\/mfrac><\/mrow><\/msqrt><\/mrow><\/math><xml>     <\/xml>  <\/p>","correct":false},{"option":"<p>    <math><mrow><msup><mrow><mrow><mo>(<\/mo><mrow><mfrac><mrow><mn>3<\/mn><msub><mi>V<\/mi><mn>0<\/mn><\/msub><\/mrow><mrow><mn>2<\/mn><mi>\u03b1<\/mi><\/mrow><\/mfrac><\/mrow><mo>)<\/mo><\/mrow><\/mrow><mrow><mn>1<\/mn><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/math><xml>     <\/xml>  <\/p>","correct":false},{"option":"<p>    <math><mrow><msqrt><mrow><mfrac><mrow><mn>3<\/mn><msub><mi>V<\/mi><mn>0<\/mn><\/msub><msup><mrow><\/mrow><mn>2<\/mn><\/msup><\/mrow><mrow><mn>2<\/mn><mi>\u03b1<\/mi><\/mrow><\/mfrac><\/mrow><\/msqrt><\/mrow><\/math><xml>     <\/xml>  <\/p>","correct":false},{"option":"<p>    <math><mrow><msup><mrow><mrow><mo>(<\/mo><mrow><mfrac><mrow><mn>3<\/mn><msub><mi>V<\/mi><mn>0<\/mn><\/msub><msup><mrow><\/mrow><mn>2<\/mn><\/msup><\/mrow><mrow><mn>2<\/mn><mi>\u03b1<\/mi><\/mrow><\/mfrac><\/mrow><mo>)<\/mo><\/mrow><\/mrow><mrow><mn>1<\/mn><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/math><xml>     <\/xml>  <\/p>","correct":true}],"solution":"<p>    <math><mrow><mi>a<\/mi><mo>=<\/mo><mfrac><mrow><mi>d<\/mi><mi>v<\/mi><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>d<\/mi><mi>v<\/mi><\/mrow><mrow><mi>d<\/mi><mi>x<\/mi><\/mrow><\/mfrac><mo>.<\/mo><mfrac><mrow><mi>d<\/mi><mi>x<\/mi><\/mrow><mrow><mi>d<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mi>V<\/mi><mo>.<\/mo><mfrac><mrow><mi>d<\/mi><mi>v<\/mi><\/mrow><mrow><mi>d<\/mi><mi>x<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mo>\u2212<\/mo><mi>\u03b1<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mrow><\/math><xml>     <\/xml>  <\/p><p><math><mrow><mstyle displaystyle=\"true\"><mrow><munderover><mo>\u222b<\/mo><mrow><msub><mi>v<\/mi><mn>0<\/mn><\/msub><\/mrow><mn>0<\/mn><\/munderover><mrow><mi>V<\/mi><mi>d<\/mi><mi>v<\/mi><\/mrow><\/mrow><\/mstyle><mo>=<\/mo><mo>\u2212<\/mo><mi>\u03b1<\/mi><mstyle displaystyle=\"true\"><mrow><munderover><mo>\u222b<\/mo><mn>0<\/mn><mi>s<\/mi><\/munderover><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mi>d<\/mi><mi>x<\/mi><\/mrow><\/mrow><\/mstyle><\/mrow><\/math><xml>     <\/xml><\/p>  <p><math><mrow><msubsup><mrow><mrow><mo>[<\/mo><mrow><mfrac><mrow><msubsup><mi>V<\/mi><mn>0<\/mn><mn>2<\/mn><\/msubsup><\/mrow><mn>2<\/mn><\/mfrac><\/mrow><mo>]<\/mo><\/mrow><\/mrow><mrow><msub><mi>v<\/mi><mn>0<\/mn><\/msub><\/mrow><mn>0<\/mn><\/msubsup><mo>=<\/mo><mo>\u2212<\/mo><mi>\u03b1<\/mi><msubsup><mrow><mrow><mo>[<\/mo><mrow><mfrac><mrow><msup><mi>x<\/mi><mn>3<\/mn><\/msup><\/mrow><mn>3<\/mn><\/mfrac><\/mrow><mo>]<\/mo><\/mrow><\/mrow><mn>0<\/mn><mi>s<\/mi><\/msubsup><\/mrow><\/math><xml>     <\/xml><\/p>  <p><math><mrow><mfrac><mrow><msubsup><mi>V<\/mi><mn>0<\/mn><mn>2<\/mn><\/msubsup><\/mrow><mn>2<\/mn><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>\u03b1<\/mi><msup><mi>S<\/mi><mn>3<\/mn><\/msup><\/mrow><mn>3<\/mn><\/mfrac><\/mrow><\/math><xml>     <\/xml><\/p>  <p><math><mrow><mi>S<\/mi><mo>=<\/mo><msup><mrow><mrow><mo>[<\/mo><mrow><mfrac><mrow><mn>3<\/mn><msub><mi>V<\/mi><mn>0<\/mn><\/msub><msup><mrow><\/mrow><mn>2<\/mn><\/msup><\/mrow><mrow><mn>2<\/mn><mi>\u03b1<\/mi><\/mrow><\/mfrac><\/mrow><mo>]<\/mo><\/mrow><\/mrow><mrow><mn>1<\/mn><mo>\/<\/mo><mn>3<\/mn><\/mrow><\/msup><\/mrow><\/math><xml>     <\/xml><\/p>  <p><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A particle projected with velocity V0   along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2   . The distance at which the particle stops is - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"A particle projected with velocity V0 along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2 . The distance at which the particle stops is\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A particle projected with velocity V0   along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2   . The distance at which the particle stops is - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"A particle projected with velocity V0 along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2 . The distance at which the particle stops is\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"A particle projected with velocity V0   along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2   . The distance at which the particle stops is - Infinity Learn by Sri Chaitanya","description":"A particle projected with velocity V0 along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2 . The distance at which the particle stops is","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/","og_locale":"en_US","og_type":"article","og_title":"A particle projected with velocity V0   along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2   . The distance at which the particle stops is - Infinity Learn by Sri Chaitanya","og_description":"A particle projected with velocity V0 along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2 . The distance at which the particle stops is","og_url":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@InfinityLearn_","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/","name":"A particle projected with velocity V0 along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2 . The distance at which the particle stops is - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2022-09-10T05:43:43+00:00","dateModified":"2022-09-10T05:43:43+00:00","description":"A particle projected with velocity V0 along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2 . The distance at which the particle stops is","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-projected-with-velocity-v0-----along-x-axis-the\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"A particle projected with velocity V0 along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e a=\u2212\u03b1x2 . The distance at which the particle stops is"}]}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions\/254234"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/questions"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/questions"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=254234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=254234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}