{"id":259583,"date":"2022-09-10T12:16:34","date_gmt":"2022-09-10T06:46:34","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/a-particle-is-moving-such-that-its-position-coordinates-xy-are-2m-3m-at-time-t-2s-and-13-m-14m-at-time-t-5saverage-velocity-vector-v%e2%86%92av-from-t-0-to-t-5-s-is\/"},"modified":"2022-09-10T12:16:34","modified_gmt":"2022-09-10T06:46:34","slug":"a-particle-is-moving-such-that-its-position-coordinates-xy-are-2m-3m-at-time-t-2s-and-13-m-14m-at-time-t-5saverage-velocity-vector-v%e2%86%92av-from-t-0-to-t-5-s-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/a-particle-is-moving-such-that-its-position-coordinatesxy\/","title":{"rendered":"A particle is moving such that its position coordinates\u00a0(x,y) are (2m, 3m) at time t = 2s and (13 m, 14m) at time t = 5sAverage velocity vector\u00a0v\u2192av\u00a0from t = 0 to t = 5 s is\u00a0"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"A particle is moving such that its position coordinates\u00a0(x,y) are (2m, 3m) at time t = 2s and (13 m, 14m) at time t = 5sAverage velocity vector\u00a0v\u2192av\u00a0from t = 0 to t = 5 s is\u00a0","custom_permalink":"question\/physics\/a-particle-is-moving-such-that-its-position-coordinatesxy\/"},"categories":[],"acf":{"question":"<p>A particle is moving such that its position coordinates&nbsp;(x,y) are (2m, 3m) at time t = 2s and (13 m, 14m) at time t = 5s<\/p><p>Average velocity vector&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced separators=\"|\"><msub><mover accent=\"true\"><mi>v<\/mi><mo stretchy=\"false\">\u2192<\/mo><\/mover><mi>av<\/mi><\/msub><\/mfenced><\/math>&nbsp;from t = 0 to t = 5 s is&nbsp;<\/p>","options":[{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>1<\/mn><mn>5<\/mn><\/mfrac><mo>(<\/mo><mn>13<\/mn><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mn>14<\/mn><mover><mi>j<\/mi><mo>^<\/mo><\/mover><mo>)<\/mo><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>7<\/mn><mn>3<\/mn><\/mfrac><mo>(<\/mo><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mover><mi>j<\/mi><mo>^<\/mo><\/mover><mo>)<\/mo><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>2<\/mn><mo>(<\/mo><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mover><mi>j<\/mi><mo>^<\/mo><\/mover><mo>)<\/mo><\/math><\/p>","correct":false},{"option":"<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfrac><mn>11<\/mn><mn>5<\/mn><\/mfrac><mo>(<\/mo><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mover><mi>j<\/mi><mo>^<\/mo><\/mover><mo>)<\/mo><\/math><\/p>","correct":true}],"solution":"<p>At time t = 0, the position vector of the particle is&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mover accent=\"true\"><mi>r<\/mi><mo stretchy=\"false\">\u2192<\/mo><\/mover><mn>1<\/mn><\/msub><mo>=<\/mo><mn>2<\/mn><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mn>3<\/mn><mover><mi>j<\/mi><mo>^<\/mo><\/mover><\/math><\/p><p>At time t = 5s, the position vector of the particle is&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mover accent=\"true\"><mi>r<\/mi><mo stretchy=\"false\">\u2192<\/mo><\/mover><mn>2<\/mn><\/msub><mo>=<\/mo><mn>13<\/mn><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mn>14<\/mn><mover><mi>j<\/mi><mo>^<\/mo><\/mover><\/math><\/p><p>Displacement from&nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mover accent=\"true\"><mi>r<\/mi><mo stretchy=\"false\">\u2192<\/mo><\/mover><mn>1<\/mn><\/msub><mtext>&nbsp;to&nbsp;<\/mtext><msub><mover accent=\"true\"><mi>r<\/mi><mo stretchy=\"false\">\u2192<\/mo><\/mover><mn>2<\/mn><\/msub><\/math>&nbsp;is<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi mathvariant=\"normal\">\u0394<\/mi><mover accent=\"true\"><mi>r<\/mi><mo stretchy=\"false\">\u2192<\/mo><\/mover><mo>=<\/mo><msub><mover accent=\"true\"><mi>r<\/mi><mo stretchy=\"false\">\u2192<\/mo><\/mover><mn>2<\/mn><\/msub><mo>\u2212<\/mo><msub><mover accent=\"true\"><mi>r<\/mi><mo stretchy=\"false\">\u2192<\/mo><\/mover><mn>1<\/mn><\/msub><mo>=<\/mo><mo>(<\/mo><mn>13<\/mn><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mn>14<\/mn><mover><mi>j<\/mi><mo>^<\/mo><\/mover><mo>)<\/mo><mo>\u2212<\/mo><mo>(<\/mo><mn>2<\/mn><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mn>3<\/mn><mover><mi>j<\/mi><mo>^<\/mo><\/mover><mo>)<\/mo><mo>=<\/mo><mn>113<\/mn><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mn>11<\/mn><mover><mi>j<\/mi><mo>^<\/mo><\/mover><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo>\u2234<\/mo><\/math>Average velocity,&nbsp;<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mover accent=\"true\"><mi>v<\/mi><mo stretchy=\"false\">\u2192<\/mo><\/mover><mi>av<\/mi><\/msub><mo>=<\/mo><mfrac><mrow><mi mathvariant=\"normal\">\u0394<\/mi><mover accent=\"true\"><mi>r<\/mi><mo stretchy=\"false\">\u2192<\/mo><\/mover><\/mrow><mrow><mi mathvariant=\"normal\">\u0394<\/mi><mi>t<\/mi><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>11<\/mn><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mn>11<\/mn><mover><mi>j<\/mi><mo>^<\/mo><\/mover><\/mrow><mrow><mn>5<\/mn><mo>\u2212<\/mo><mn>0<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>11<\/mn><mn>5<\/mn><\/mfrac><mo>(<\/mo><mover><mi>i<\/mi><mo>^<\/mo><\/mover><mo>+<\/mo><mover><mi>j<\/mi><mo>^<\/mo><\/mover><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>A particle is moving such that its position coordinates\u00a0(x,y) 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