{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-16T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":61187,"title":"Estimate brake disc temperature rise during braking.","description":"During braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can lead to brake fade and reduced braking effectiveness.\r\nGiven braking energy absorbed by the disc, disc mass, and material heat capacity, estimate the resulting temperature increase.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 383px 21px; text-align: left; transform-origin: 383px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDuring braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can lead to brake fade and reduced braking effectiveness.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 383px 21px; text-align: left; transform-origin: 383px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven braking energy absorbed by the disc, disc mass, and material heat capacity, estimate the resulting temperature increase.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function dT = brakeDiscTempRise(E, m, Cp)\r\ndT = 0;\r\nend\r\n","test_suite":"%%\r\nE = 150000; m = 7; Cp = 500;\r\ndT_correct = 42.8571;\r\nassert(abs(brakeDiscTempRise(E,m,Cp)-dT_correct) \u003c 1e-3)\r\n\r\n%%\r\nE = 100000; m = 5; Cp = 450;\r\ndT_correct = 44.4444;\r\nassert(abs(brakeDiscTempRise(E,m,Cp)-dT_correct) \u003c 1e-3)\r\n\r\n%%\r\nE = 0; m = 6; Cp = 500;\r\ndT_correct = 0;\r\nassert(isequal(brakeDiscTempRise(E,m,Cp),dT_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-02-02T07:26:30.000Z","updated_at":"2026-04-14T21:22:08.000Z","published_at":"2026-02-02T07:26:30.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDuring braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can lead to brake fade and reduced braking effectiveness.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven braking energy absorbed by the disc, disc mass, and material heat capacity, estimate the resulting temperature increase.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61186,"title":"Compute optimal front–rear brake force distribution.","description":"Modern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping distance, and prevent wheel lock.\r\nGiven total braking demand and axle load distribution, compute the optimal front and rear brake force allocation that preserves balance and traction.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 383px 21px; text-align: left; transform-origin: 383px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eModern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping distance, and prevent wheel lock.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 383px 21px; text-align: left; transform-origin: 383px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven total braking demand and axle load distribution, compute the optimal front and rear brake force allocation that preserves balance and traction.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Ff, Fr] = brakeDistribution(F_total, front_ratio)\r\nFf = 0; Fr = 0;\r\nend\r\n","test_suite":"%%\r\nF_total = 6000; front_ratio = 0.6;\r\n[Ff,Fr] = brakeDistribution(F_total,front_ratio);\r\nassert(isequal([Ff Fr],[3600 2400]))\r\n\r\n%%\r\nF_total = 8000; front_ratio = 0.7;\r\n[Ff,Fr] = brakeDistribution(F_total,front_ratio);\r\nassert(isequal([Ff Fr],[5600 2400]))\r\n\r\n%%\r\nF_total = 0; front_ratio = 0.6;\r\n[Ff,Fr] = brakeDistribution(F_total,front_ratio);\r\nassert(isequal([Ff Fr],[0 0]))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-02-02T06:39:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-02-02T06:39:14.000Z","updated_at":"2026-04-18T04:57:11.000Z","published_at":"2026-02-02T06:39:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eModern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping distance, and prevent wheel lock.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven total braking demand and axle load distribution, compute the optimal front and rear brake force allocation that preserves balance and traction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44365,"title":"An asteroid and a spacecraft","description":"\r\n\u0026#128640 Imagine a non-relativistic simple situation. \r\n\r\nAssume positions p0, p1, p2, and p3 are three dimensional Cartesian coordinates.\r\n\r\nYour spacecraft started from the position p0 at time t0. \r\n\r\nYour spacecraft is moving with a constant velocity.\r\n\r\nYour spacecraft is expected to reach a star at the location p1 at time t1.\r\n\r\nYou just heard over the radio that an asteroid has been identified at the location p2 at time t0.\r\n\r\nThe asteroid is moving with a constant velocity.\r\n\r\nThe asteroid is expected to reach another star at the location p3 at time t1. \r\n\r\nYou need to write a code 'safetrip' in MATLAB to return true if the minimum distance between your spacecraft and the asteroid will be more than the distance d during the time interval between t0 and t1, otherwise return false.","description_html":"\u003cp\u003e\u0026#128640 Imagine a non-relativistic simple situation.\u003c/p\u003e\u003cp\u003eAssume positions p0, p1, p2, and p3 are three dimensional Cartesian coordinates.\u003c/p\u003e\u003cp\u003eYour spacecraft started from the position p0 at time t0.\u003c/p\u003e\u003cp\u003eYour spacecraft is moving with a constant velocity.\u003c/p\u003e\u003cp\u003eYour spacecraft is expected to reach a star at the location p1 at time t1.\u003c/p\u003e\u003cp\u003eYou just heard over the radio that an asteroid has been identified at the location p2 at time t0.\u003c/p\u003e\u003cp\u003eThe asteroid is moving with a constant velocity.\u003c/p\u003e\u003cp\u003eThe asteroid is expected to reach another star at the location p3 at time t1.\u003c/p\u003e\u003cp\u003eYou need to write a code 'safetrip' in MATLAB to return true if the minimum distance between your spacecraft and the asteroid will be more than the distance d during the time interval between t0 and t1, otherwise return false.\u003c/p\u003e","function_template":"function ok = safetrip(d, t0, t1, p0, p1, p2, p3)\r\n    if d\u003e1000000000\r\n        ok = true;\r\n    end\r\nend","test_suite":"%%\r\np0 = [0 0 0];\r\np1 = [1 1 1];\r\np2 = [2 2 2];\r\np3 = [3 3 3];\r\nt0 = 0; \r\nt1 = 1;\r\nd = 1;\r\nok = true;\r\nassert(isequal(safetrip(d, t0, t1, p0, p1, p2, p3), ok))\r\n\r\n%%\r\np0 = [3 3 3];\r\np1 = [2 2 2];\r\np2 = [2 2 2];\r\np3 = [3 3 3];\r\nt0 = 0; \r\nt1 = 1;\r\nd = 1;\r\nok = false;\r\nassert(isequal(safetrip(d, t0, t1, p0, p1, p2, p3), ok))\r\n\r\n%%\r\np0 = [1 2 3];\r\np1 = [4 5 6];\r\np2 = [3 2 1];\r\np3 = [6 5 4];\r\nt0 = 10; \r\nt1 = 20;\r\nd = 2;\r\nok = true;\r\nassert(isequal(safetrip(d, t0, t1, p0, p1, p2, p3), ok))\r\n\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":8,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":180,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-10T02:30:44.000Z","updated_at":"2026-04-18T10:51:25.000Z","published_at":"2017-10-16T01:51:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026amp;#128640 Imagine a non-relativistic simple situation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume positions p0, p1, p2, and p3 are three dimensional Cartesian coordinates.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour spacecraft started from the position p0 at time t0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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velocity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe asteroid is expected to reach another star at the location p3 at time t1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou need to write a code 'safetrip' in MATLAB to return true if the minimum distance between your spacecraft and the asteroid will be more than the distance d during the time interval between t0 and t1, otherwise return false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" 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Excessive temperature rise can lead to brake fade and reduced braking effectiveness.\r\nGiven braking energy absorbed by the disc, disc mass, and material heat capacity, estimate the resulting temperature increase.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 383px 21px; text-align: left; transform-origin: 383px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDuring braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can lead to brake fade and reduced braking effectiveness.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 383px 21px; text-align: left; transform-origin: 383px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven braking energy absorbed by the disc, disc mass, and material heat capacity, estimate the resulting temperature increase.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function dT = brakeDiscTempRise(E, m, Cp)\r\ndT = 0;\r\nend\r\n","test_suite":"%%\r\nE = 150000; m = 7; Cp = 500;\r\ndT_correct = 42.8571;\r\nassert(abs(brakeDiscTempRise(E,m,Cp)-dT_correct) \u003c 1e-3)\r\n\r\n%%\r\nE = 100000; m = 5; Cp = 450;\r\ndT_correct = 44.4444;\r\nassert(abs(brakeDiscTempRise(E,m,Cp)-dT_correct) \u003c 1e-3)\r\n\r\n%%\r\nE = 0; m = 6; Cp = 500;\r\ndT_correct = 0;\r\nassert(isequal(brakeDiscTempRise(E,m,Cp),dT_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":43,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-02-02T07:26:30.000Z","updated_at":"2026-04-14T21:22:08.000Z","published_at":"2026-02-02T07:26:30.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDuring braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can lead to brake fade and reduced braking effectiveness.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven braking energy absorbed by the disc, disc mass, and material heat capacity, estimate the resulting temperature increase.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61186,"title":"Compute optimal front–rear brake force distribution.","description":"Modern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping distance, and prevent wheel lock.\r\nGiven total braking demand and axle load distribution, compute the optimal front and rear brake force allocation that preserves balance and traction.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 383px 21px; text-align: left; transform-origin: 383px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eModern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping distance, and prevent wheel lock.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 383px 21px; text-align: left; transform-origin: 383px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven total braking demand and axle load distribution, compute the optimal front and rear brake force allocation that preserves balance and traction.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [Ff, Fr] = brakeDistribution(F_total, front_ratio)\r\nFf = 0; Fr = 0;\r\nend\r\n","test_suite":"%%\r\nF_total = 6000; front_ratio = 0.6;\r\n[Ff,Fr] = brakeDistribution(F_total,front_ratio);\r\nassert(isequal([Ff Fr],[3600 2400]))\r\n\r\n%%\r\nF_total = 8000; front_ratio = 0.7;\r\n[Ff,Fr] = brakeDistribution(F_total,front_ratio);\r\nassert(isequal([Ff Fr],[5600 2400]))\r\n\r\n%%\r\nF_total = 0; front_ratio = 0.6;\r\n[Ff,Fr] = brakeDistribution(F_total,front_ratio);\r\nassert(isequal([Ff Fr],[0 0]))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2305225,"edited_by":2305225,"edited_at":"2026-02-02T06:39:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":36,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-02-02T06:39:14.000Z","updated_at":"2026-04-18T04:57:11.000Z","published_at":"2026-02-02T06:39:17.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eModern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping distance, and prevent wheel lock.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven total braking demand and axle load distribution, compute the optimal front and rear brake force allocation that preserves balance and traction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44365,"title":"An asteroid and a spacecraft","description":"\r\n\u0026#128640 Imagine a non-relativistic simple situation. \r\n\r\nAssume positions p0, p1, p2, and p3 are three dimensional Cartesian coordinates.\r\n\r\nYour spacecraft started from the position p0 at time t0. \r\n\r\nYour spacecraft is moving with a constant velocity.\r\n\r\nYour spacecraft is expected to reach a star at the location p1 at time t1.\r\n\r\nYou just heard over the radio that an asteroid has been identified at the location p2 at time t0.\r\n\r\nThe asteroid is moving with a constant velocity.\r\n\r\nThe asteroid is expected to reach another star at the location p3 at time t1. \r\n\r\nYou need to write a code 'safetrip' in MATLAB to return true if the minimum distance between your spacecraft and the asteroid will be more than the distance d during the time interval between t0 and t1, otherwise return false.","description_html":"\u003cp\u003e\u0026#128640 Imagine a non-relativistic simple situation.\u003c/p\u003e\u003cp\u003eAssume positions p0, p1, p2, and p3 are three dimensional Cartesian coordinates.\u003c/p\u003e\u003cp\u003eYour spacecraft started from the position p0 at time t0.\u003c/p\u003e\u003cp\u003eYour spacecraft is moving with a constant velocity.\u003c/p\u003e\u003cp\u003eYour spacecraft is expected to reach a star at the location p1 at time t1.\u003c/p\u003e\u003cp\u003eYou just heard over the radio that an asteroid has been identified at the location p2 at time t0.\u003c/p\u003e\u003cp\u003eThe asteroid is moving with a constant velocity.\u003c/p\u003e\u003cp\u003eThe asteroid is expected to reach another star at the location p3 at time t1.\u003c/p\u003e\u003cp\u003eYou need to write a code 'safetrip' in MATLAB to return true if the minimum distance between your spacecraft and the asteroid will be more than the distance d during the time interval between t0 and t1, otherwise return false.\u003c/p\u003e","function_template":"function ok = safetrip(d, t0, t1, p0, p1, p2, p3)\r\n    if d\u003e1000000000\r\n        ok = true;\r\n    end\r\nend","test_suite":"%%\r\np0 = [0 0 0];\r\np1 = [1 1 1];\r\np2 = [2 2 2];\r\np3 = [3 3 3];\r\nt0 = 0; \r\nt1 = 1;\r\nd = 1;\r\nok = true;\r\nassert(isequal(safetrip(d, t0, t1, p0, p1, p2, p3), ok))\r\n\r\n%%\r\np0 = [3 3 3];\r\np1 = [2 2 2];\r\np2 = [2 2 2];\r\np3 = [3 3 3];\r\nt0 = 0; \r\nt1 = 1;\r\nd = 1;\r\nok = false;\r\nassert(isequal(safetrip(d, t0, t1, p0, p1, p2, p3), ok))\r\n\r\n%%\r\np0 = [1 2 3];\r\np1 = [4 5 6];\r\np2 = [3 2 1];\r\np3 = [6 5 4];\r\nt0 = 10; \r\nt1 = 20;\r\nd = 2;\r\nok = true;\r\nassert(isequal(safetrip(d, t0, t1, p0, p1, p2, p3), ok))\r\n\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":8,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":180,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-10T02:30:44.000Z","updated_at":"2026-04-18T10:51:25.000Z","published_at":"2017-10-16T01:51:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026amp;#128640 Imagine a non-relativistic simple situation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume positions p0, p1, p2, and p3 are three dimensional Cartesian coordinates.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour spacecraft started from the position p0 at time t0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour spacecraft is moving with a constant velocity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour spacecraft is expected to reach a star at the location p1 at time t1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou just heard over the radio that an asteroid has been identified at the location p2 at time t0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe asteroid is moving with a constant 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