{"id":337924,"date":"2023-01-06T10:07:37","date_gmt":"2023-01-06T04:37:37","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-displacement-time-graph-for-two-particles-a-and-b-are-straight-lines-inclined-at-angles-of-30o-and-60o-with-the-time-axis-the-ratio-of-their-velocities-is\/"},"modified":"2025-06-30T11:02:31","modified_gmt":"2025-06-30T05:32:31","slug":"the-displacement-time-graph-for-two-particles-a-and-b-are-straight-lines-inclined-at-angles-of-30o-and-60o-with-the-time-axis-the-ratio-of-their-velocities-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/the-displacement-time-graph-for-two-particles-a-and-b-are-st\/","title":{"rendered":"The displacement-time graph for two particles A and B are straight lines inclined at angles of 30o and 60o with the time axis. The ratio of their velocities is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"displacement-time graph","_yoast_wpseo_title":"The displacement-time graph for two particles A and B are straight lines","_yoast_wpseo_metadesc":"The displacement-time graph for two particles A and B are straight lines inclined at angles of 30 degrees and 60 degrees with the time axis.","custom_permalink":"question\/physics\/the-displacement-time-graph-for-two-particles-a-and-b-are-st\/"},"categories":[],"acf":{"question":"

The displacement-time graph for two particles <\/span>A <\/span>and <\/span>B <\/span>are straight lines inclined at angles of <\/span>3<\/mn>0<\/mn><\/mrow>o<\/mi><\/mrow><\/msup><\/math> and <\/span>6<\/mn>0<\/mn><\/mrow>o<\/mi><\/mrow><\/msup><\/math> with the time axis. The ratio of their velocities is<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:8pt;line-height:108%;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal;font-size:12pt\">","options":[{"option":"1<\/mn>:<\/mo>2<\/mn><\/math>","correct":false},{"option":"1<\/mn>:<\/mo>3<\/mn><\/mrow><\/msqrt><\/math>","correct":false},{"option":"3<\/mn><\/mrow><\/msqrt>:<\/mo>1<\/mn> <\/mi><\/math>","correct":false},{"option":"1<\/mn>:<\/mo>3<\/mn><\/math> <\/span>","correct":true}],"solution":"The displacement-time graph for two particles A and B are straight lines inclined at angles of\r\n\r\n3<\/mn>0<\/mn><\/mrow>o<\/mi><\/mrow><\/msup><\/math>\r\n\r\nand\r\n\r\n6<\/mn>0<\/mn><\/mrow>o<\/mi><\/mrow><\/msup><\/math>\r\n\r\nwith the time axis. The ratio of their velocities is\r\n\r\n1<\/mn>:<\/mo>3<\/mn><\/math>\r\n\r\n.\r\nLet\r\n\r\nv<\/mi><\/mrow>A<\/mi><\/mrow><\/msub>\u00a0<\/mi><\/math>\r\n\r\nand\r\n\r\n\u00a0<\/mi>v<\/mi><\/mrow>B<\/mi><\/mrow><\/msub><\/math>\r\n\r\nbe the velocity of particles A and B respectively.\r\nSo\r\n\r\nv<\/mi><\/mrow>A<\/mi><\/mrow><\/msub>\u00a0<\/mi>:<\/mo>\u00a0<\/mi>v<\/mi><\/mrow>B<\/mi><\/mrow><\/msub>=<\/mo>Slope<\/mi><\/mrow>A<\/mi><\/mrow><\/msub>:<\/mo>Slope<\/mi><\/mrow>B<\/mi><\/mrow><\/msub><\/math>\r\n\r\nAlso,\r\n\r\nSlope<\/mi><\/mrow>A<\/mi><\/mrow><\/msub>:<\/mo>Slope<\/mi><\/mrow>B<\/mi><\/mrow><\/msub>=<\/mo>tan<\/mi>30<\/mn>\u00b0<\/mo>:<\/mo>tan<\/mi>60<\/mn><\/math>\r\n\r\n \r\n\r\n=<\/mo>><\/mo>v<\/mi><\/mrow>A<\/mi><\/mrow><\/msub>\u00a0<\/mi>:<\/mo>\u00a0<\/mi>v<\/mi><\/mrow>B<\/mi><\/mrow><\/msub>=<\/mo>tan<\/mi>30<\/mn>\u00b0<\/mo>:<\/mo>tan<\/mi>60<\/mn>\u00b0<\/mo><\/math>\r\n\r\n \r\n\r\n=<\/mo>><\/mo>v<\/mi><\/mrow>A<\/mi><\/mrow><\/msub>\u00a0<\/mi>:<\/mo>\u00a0<\/mi>v<\/mi><\/mrow>B<\/mi><\/mrow><\/msub>=<\/mo>1<\/mn><\/mrow>3<\/mn><\/mrow><\/msqrt><\/mrow><\/mfrac>\u00a0<\/mi>:<\/mo>\u00a0<\/mi>3<\/mn><\/mrow><\/msqrt><\/math>\r\n\r\n \r\n\r\n=<\/mo>><\/mo>v<\/mi><\/mrow>A<\/mi><\/mrow><\/msub>\u00a0<\/mi>:<\/mo>\u00a0<\/mi>v<\/mi><\/mrow>B<\/mi><\/mrow><\/msub>=<\/mo>1<\/mn>:<\/mo>3<\/mn><\/math>\r\n","subject":""},"yoast_head":"\nThe 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