{"id":261125,"date":"2022-09-10T12:34:45","date_gmt":"2022-09-10T07:04:45","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-velocity-v-of-a-particle-depends-upon-the-time-t-according-to-the-equation-vabtcdt-write-the-dimensions-of-a-b-c-and-d\/"},"modified":"2022-09-10T12:34:45","modified_gmt":"2022-09-10T07:04:45","slug":"the-velocity-v-of-a-particle-depends-upon-the-time-t-according-to-the-equation-vabtcdt-write-the-dimensions-of-a-b-c-and-d","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/the-velocityvof-a-particle-depends-upon-the-time-t-accordi\/","title":{"rendered":"The velocity\u00a0v\u00a0of a particle depends upon the time t according to the equation,\u00a0v=a+bt+cd+t. Write the dimensions of\u00a0\u00a0a,\u00a0b,\u00a0c\u00a0and\u00a0d."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The velocity\u00a0v\u00a0of a particle depends upon the time t according to the equation,\u00a0v=a+bt+cd+t. Write the dimensions of\u00a0\u00a0a,\u00a0b,\u00a0c\u00a0and\u00a0d.","custom_permalink":"question\/physics\/the-velocityvof-a-particle-depends-upon-the-time-t-accordi\/"},"categories":[],"acf":{"question":"<p>The velocity&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><\/math>&nbsp;of a particle depends upon the time t according to the equation,&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>v<\/mi><mo>=<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mi>t<\/mi><mo>+<\/mo><mfrac><mi>c<\/mi><mrow><mi>d<\/mi><mo>+<\/mo><mi>t<\/mi><\/mrow><\/mfrac><\/math>. Write the dimensions of&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>&nbsp;<\/mo><mi>a<\/mi><mo>,<\/mo><mo>&nbsp;<\/mo><mi>b<\/mi><mo>,<\/mo><mo>&nbsp;<\/mo><mi>c<\/mi><mo>&nbsp;<\/mo><mi>a<\/mi><mi>n<\/mi><mi>d<\/mi><mo>&nbsp;<\/mo><mi>d<\/mi><\/math>.<\/p>","options":[{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>[<\/mo><mi>a<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi>v<\/mi><mo>]<\/mo><mo>,<\/mo><mo>[<\/mo><mi>b<\/mi><mo>]<\/mo><mo>=<\/mo><mfenced close=\"]\" open=\"[\"><msup><mi>LT<\/mi><mn>2<\/mn><\/msup><\/mfenced><mo>,<\/mo><mo>[<\/mo><mi>c<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi mathvariant=\"normal\">L<\/mi><mo>]<\/mo><mo>,<\/mo><mo>[<\/mo><mi>d<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi mathvariant=\"normal\">T<\/mi><mo>]<\/mo><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>[<\/mo><mi>a<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi>v<\/mi><mo>]<\/mo><mo>,<\/mo><mo>[<\/mo><mi>b<\/mi><mo>]<\/mo><mo>=<\/mo><mfenced close=\"]\" open=\"[\"><msup><mi>LT<\/mi><mrow><mo>-<\/mo><mn>2<\/mn><\/mrow><\/msup><\/mfenced><mo>,<\/mo><mo>[<\/mo><mi>c<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi mathvariant=\"normal\">L<\/mi><mo>]<\/mo><mo>,<\/mo><mo>[<\/mo><mi>d<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi mathvariant=\"normal\">T<\/mi><mo>]<\/mo><\/math><\/p>","correct":true},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>[<\/mo><mi>a<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi>v<\/mi><mo>]<\/mo><mo>,<\/mo><mo>[<\/mo><mi>b<\/mi><mo>]<\/mo><mo>=<\/mo><mfenced close=\"]\" open=\"[\"><msup><mi>LT<\/mi><mrow><mo>-<\/mo><mn>2<\/mn><\/mrow><\/msup><\/mfenced><mo>,<\/mo><mo>[<\/mo><mi>c<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi mathvariant=\"normal\">L<\/mi><mo>]<\/mo><mo>,<\/mo><mo>[<\/mo><mi>d<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi mathvariant=\"normal\">L<\/mi><mo>]<\/mo><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>[<\/mo><mi>a<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi>v<\/mi><mo>]<\/mo><mo>,<\/mo><mo>[<\/mo><mi>b<\/mi><mo>]<\/mo><mo>=<\/mo><mfenced close=\"]\" open=\"[\"><msup><mi>LT<\/mi><mrow><mo>-<\/mo><mn>3<\/mn><\/mrow><\/msup><\/mfenced><mo>,<\/mo><mo>[<\/mo><mi>c<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi mathvariant=\"normal\">L<\/mi><mo>]<\/mo><mo>,<\/mo><mo>[<\/mo><mi>d<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi mathvariant=\"normal\">T<\/mi><mo>]<\/mo><\/math><\/p>","correct":false}],"solution":"<p>From principle of homogeneity,<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>[<\/mo><mi>a<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi>v<\/mi><mo>]<\/mo><mspace linebreak=\"newline\">&nbsp;<\/mspace><mi>o<\/mi><mi>r<\/mi><mspace linebreak=\"newline\">&nbsp;<\/mspace><mo>[<\/mo><mi>a<\/mi><mo>]<\/mo><mo>=<\/mo><mfenced close=\"]\" open=\"[\"><msup><mi>LT<\/mi><mrow><mo>-<\/mo><mn>1<\/mn><\/mrow><\/msup><\/mfenced><mspace linebreak=\"newline\">&nbsp;<\/mspace><mo>[<\/mo><mi>b<\/mi><mi>t<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi>v<\/mi><mo>]<\/mo><mspace linebreak=\"newline\">&nbsp;<\/mspace><mi>o<\/mi><mi>r<\/mi><mspace linebreak=\"newline\">&nbsp;<\/mspace><mo>[<\/mo><mi>b<\/mi><mo>]<\/mo><mo>=<\/mo><mfrac><mrow><mo>[<\/mo><mi>v<\/mi><mo>]<\/mo><\/mrow><mrow><mo>[<\/mo><mi>t<\/mi><mo>]<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mfenced close=\"]\" open=\"[\"><msup><mi>LT<\/mi><mrow><mo>-<\/mo><mn>1<\/mn><\/mrow><\/msup><\/mfenced><mrow><mo>[<\/mo><mi mathvariant=\"normal\">T<\/mi><mo>]<\/mo><\/mrow><\/mfrac><\/math><\/p><p>or,<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>[<\/mo><mi>b<\/mi><mo>]<\/mo><mo>=<\/mo><mfenced close=\"]\" open=\"[\"><msup><mi>LT<\/mi><mrow><mo>-<\/mo><mn>2<\/mn><\/mrow><\/msup><\/mfenced><\/math><\/p><p>Similarly,<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>[<\/mo><mi>d<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi>t<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi mathvariant=\"normal\">T<\/mi><mo>]<\/mo><\/math><\/p><p>Further,<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mrow><mo>[<\/mo><mi>c<\/mi><mo>]<\/mo><\/mrow><mrow><mo>[<\/mo><mi>d<\/mi><mo>+<\/mo><mi>t<\/mi><mo>]<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mo>[<\/mo><mi>v<\/mi><mo>]<\/mo><mspace linebreak=\"newline\">&nbsp;<\/mspace><mi>o<\/mi><mi>r<\/mi><mspace linebreak=\"newline\">&nbsp;<\/mspace><mo>[<\/mo><mi>c<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi>v<\/mi><mo>]<\/mo><mo>[<\/mo><mi>d<\/mi><mo>+<\/mo><mi>t<\/mi><mo>]<\/mo><\/math><\/p><p>or,&nbsp;<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>[<\/mo><mi>c<\/mi><mo>]<\/mo><mo>=<\/mo><mfenced close=\"]\" open=\"[\"><msup><mi>LT<\/mi><mrow><mo>-<\/mo><mn>1<\/mn><\/mrow><\/msup><\/mfenced><mo>[<\/mo><mi mathvariant=\"normal\">T<\/mi><mo>]<\/mo><mspace linebreak=\"newline\">&nbsp;<\/mspace><mi>o<\/mi><mi>r<\/mi><mspace linebreak=\"newline\">&nbsp;<\/mspace><mo>[<\/mo><mi>c<\/mi><mo>]<\/mo><mo>=<\/mo><mo>[<\/mo><mi mathvariant=\"normal\">L<\/mi><mo>]<\/mo><\/math><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The velocity\u00a0v\u00a0of a particle depends upon the time t according to the equation,\u00a0v=a+bt+cd+t. 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