{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":1360,"title":"Special Relativity 101.","description":"Special relativity states that the effective mass of an object varies as a function of its velocity. If *c* is the speed of light (c approx. = 300,000 km/s) and *v* is the velocity of the object (in km/s), find the effective mass m' of an object traveling at a velocity v. Assume that at v = 0 m/s, m = 1 kg.","description_html":"\u003cp\u003eSpecial relativity states that the effective mass of an object varies as a function of its velocity. If \u003cb\u003ec\u003c/b\u003e is the speed of light (c approx. = 300,000 km/s) and \u003cb\u003ev\u003c/b\u003e is the velocity of the object (in km/s), find the effective mass m' of an object traveling at a velocity v. Assume that at v = 0 m/s, m = 1 kg.\u003c/p\u003e","function_template":"function mprime = specialRelativity(v)\r\n  mprime = v;\r\nend","test_suite":"%%\r\nv = 0;\r\ny_correct = 1;\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 1000;      % km/s\r\ny_correct = 1; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 10000;          % km/s\r\ny_correct = 1.0006; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 50000;          % km/s\r\ny_correct = 1.0142; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 100000;         % km/s\r\ny_correct = 1.0607; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 200000;         % km/s\r\ny_correct = 1.3416; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 250000;         % km/s\r\ny_correct = 1.8091; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 290000;         % km/s\r\ny_correct = 3.9057; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 299000;          % km/s\r\ny_correct = 12.2577; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 299900;          % km/s\r\ny_correct = 38.7331; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 299999;           % km/s\r\ny_correct = 387.2987; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":810,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":112,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-19T00:59:56.000Z","updated_at":"2026-02-06T11:57:49.000Z","published_at":"2013-03-19T01:00:25.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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\u003eSpecial relativity states that the effective mass of an object varies as a function of its velocity. If\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the speed of light (c approx. = 300,000 km/s) and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the velocity of the object (in km/s), find the effective mass m' of an object traveling at a velocity v. Assume that at v = 0 m/s, m = 1 kg.\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\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44741,"title":"You are constantly moving at a speed v faster than your twin brother. How long does it take before you become 1s younger than him according to the theory of relativity?","description":"You are moving at a speed of v_in (km/h) relative to your twin brother of the exact (even in seconds) same age.\r\n\r\nDefine:\r\ngam = 1/sqrt(1-v^2/c^2)   where v is the relative speed in m/s and c is the speed of light in m/s.\r\n\r\nAccording to the theory of relativity (specifically time dilation), a time interval dt for your twin brother equals a time interval of gam*dt for you. For how long must you travel, in years, with the speed v_in in order to become 1 second younger than your twin brother?","description_html":"\u003cp\u003eYou are moving at a speed of v_in (km/h) relative to your twin brother of the exact (even in seconds) same age.\u003c/p\u003e\u003cp\u003eDefine:\r\ngam = 1/sqrt(1-v^2/c^2)   where v is the relative speed in m/s and c is the speed of light in m/s.\u003c/p\u003e\u003cp\u003eAccording to the theory of relativity (specifically time dilation), a time interval dt for your twin brother equals a time interval of gam*dt for you. For how long must you travel, in years, with the speed v_in in order to become 1 second younger than your twin brother?\u003c/p\u003e","function_template":"function years = becomeOneSecondYounger(v_in)\r\n    \r\nend","test_suite":"%%\r\nv_in = 100;            % km/h\r\nyearsCorrect = 241830; % years\r\nyears = becomeOneSecondYounger(v_in);\r\nassert(abs(yearsCorrect-years)\u003c10)\r\n\r\n\r\n%%\r\nv_in = 1000;           % km/h\r\nyearsCorrect = 2418.7; % years\r\nyears = becomeOneSecondYounger(v_in);\r\nassert(abs(yearsCorrect-years)\u003c0.1)\r\n\r\n%%\r\nv_in = 10000;           % km/h\r\nyearsCorrect = 24.187;  % years\r\nyears = becomeOneSecondYounger(v_in);\r\nassert(abs(yearsCorrect-years)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":195293,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2018-10-03T10:36:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-10-03T08:07:37.000Z","updated_at":"2018-10-03T10:36:13.000Z","published_at":"2018-10-03T10:32:42.000Z","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\u003eYou are moving at a speed of v_in (km/h) relative to your twin brother of the exact (even in seconds) same age.\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\u003eDefine: gam = 1/sqrt(1-v^2/c^2) where v is the relative speed in m/s and c is the speed of light in m/s.\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\u003eAccording to the theory of relativity (specifically time dilation), a time interval dt for your twin brother equals a time interval of gam*dt for you. For how long must you travel, in years, with the speed v_in in order to become 1 second younger than your twin brother?\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\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":1360,"title":"Special Relativity 101.","description":"Special relativity states that the effective mass of an object varies as a function of its velocity. 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Assume that at v = 0 m/s, m = 1 kg.\u003c/p\u003e","function_template":"function mprime = specialRelativity(v)\r\n  mprime = v;\r\nend","test_suite":"%%\r\nv = 0;\r\ny_correct = 1;\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 1000;      % km/s\r\ny_correct = 1; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 10000;          % km/s\r\ny_correct = 1.0006; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 50000;          % km/s\r\ny_correct = 1.0142; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 100000;         % km/s\r\ny_correct = 1.0607; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 200000;         % km/s\r\ny_correct = 1.3416; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 250000;         % km/s\r\ny_correct = 1.8091; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 290000;         % km/s\r\ny_correct = 3.9057; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 299000;          % km/s\r\ny_correct = 12.2577; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 299900;          % km/s\r\ny_correct = 38.7331; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)\r\n\r\n%%\r\nv = 299999;           % km/s\r\ny_correct = 387.2987; % kg\r\nassert(abs(specialRelativity(v)-y_correct) \u003c= 0.0001)","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":810,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":112,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-03-19T00:59:56.000Z","updated_at":"2026-02-06T11:57:49.000Z","published_at":"2013-03-19T01:00:25.000Z","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\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"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\\n\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\u003eSpecial relativity states that the effective mass of an object varies as a function of its velocity. If\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ec\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the speed of light (c approx. = 300,000 km/s) and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ev\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the velocity of the object (in km/s), find the effective mass m' of an object traveling at a velocity v. Assume that at v = 0 m/s, m = 1 kg.\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\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44741,"title":"You are constantly moving at a speed v faster than your twin brother. How long does it take before you become 1s younger than him according to the theory of relativity?","description":"You are moving at a speed of v_in (km/h) relative to your twin brother of the exact (even in seconds) same age.\r\n\r\nDefine:\r\ngam = 1/sqrt(1-v^2/c^2)   where v is the relative speed in m/s and c is the speed of light in m/s.\r\n\r\nAccording to the theory of relativity (specifically time dilation), a time interval dt for your twin brother equals a time interval of gam*dt for you. For how long must you travel, in years, with the speed v_in in order to become 1 second younger than your twin brother?","description_html":"\u003cp\u003eYou are moving at a speed of v_in (km/h) relative to your twin brother of the exact (even in seconds) same age.\u003c/p\u003e\u003cp\u003eDefine:\r\ngam = 1/sqrt(1-v^2/c^2)   where v is the relative speed in m/s and c is the speed of light in m/s.\u003c/p\u003e\u003cp\u003eAccording to the theory of relativity (specifically time dilation), a time interval dt for your twin brother equals a time interval of gam*dt for you. For how long must you travel, in years, with the speed v_in in order to become 1 second younger than your twin brother?\u003c/p\u003e","function_template":"function years = becomeOneSecondYounger(v_in)\r\n    \r\nend","test_suite":"%%\r\nv_in = 100;            % km/h\r\nyearsCorrect = 241830; % years\r\nyears = becomeOneSecondYounger(v_in);\r\nassert(abs(yearsCorrect-years)\u003c10)\r\n\r\n\r\n%%\r\nv_in = 1000;           % km/h\r\nyearsCorrect = 2418.7; % years\r\nyears = becomeOneSecondYounger(v_in);\r\nassert(abs(yearsCorrect-years)\u003c0.1)\r\n\r\n%%\r\nv_in = 10000;           % km/h\r\nyearsCorrect = 24.187;  % years\r\nyears = becomeOneSecondYounger(v_in);\r\nassert(abs(yearsCorrect-years)\u003c0.01)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":2,"created_by":195293,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2018-10-03T10:36:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-10-03T08:07:37.000Z","updated_at":"2018-10-03T10:36:13.000Z","published_at":"2018-10-03T10:32:42.000Z","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\u003eYou are moving at a speed of v_in (km/h) relative to your twin brother of the exact (even in seconds) same age.\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\u003eDefine: gam = 1/sqrt(1-v^2/c^2) where v is the relative speed in m/s and c is the speed of light in m/s.\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\u003eAccording to the theory of relativity (specifically time dilation), a time interval dt for your twin brother equals a time interval of gam*dt for you. 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