{"id":"cb_question_bank:740f91c1-5ba3-49c0-9df1-3b97689fa2cd","source_id":"cb_question_bank","source_item_id":"740f91c1-5ba3-49c0-9df1-3b97689fa2cd","external_id":null,"ibn":"045551-DC","question_id":"f44a29a8","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"An object’s kinetic energy, in joules, is equal to the product of one-half the object’s mass, in kilograms, and the square of the object’s speed, in meters per second. What is the speed, in meters per second, of an object with a mass of 4 kilograms and kinetic energy of 18 joules?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">An object’s kinetic energy, in joules, is equal to the product of one-half the object’s mass, in kilograms, and the square of the object’s speed, in meters per second. What is the speed, in meters per second, of an object with a mass of 4 kilograms and kinetic energy of 18 joules?</p>\n","rationale_html":"<p>Choice A is correct. It’s given that an object’s kinetic energy, in joules, is equal to the product of one-half the object’s mass, in kilograms, and the square of the object’s speed, in meters per second. This relationship can be represented by the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/606ddc7d9ac83b1fc96a669ea6fb07a4c1b572cd4845c9c903c00dd06c249bee\" alt=\"K equals, one half m v squared\"></span>, where <span class=\"italic\">K</span> is the kinetic energy, <span class=\"italic\">m </span>is the mass, and <span class=\"italic\">v </span>is the speed. Substituting a mass of 4 kilograms for <span class=\"italic\">m </span>and a kinetic energy of 18 joules for <span class=\"italic\">K </span>results in the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cea0203f95ac17cde5ef7e85476eb2208ff1af001f9370103325be960b56c835\" alt=\"18 equals, one half times 4, times v squared\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9420a056402c3f48436120d6291543b68715ae0a260fb51ff0448c55690509ab\" alt=\"18 equals, 2 v squared\"></span>. Dividing both sides of this equation by 2 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1b57d8f4ccd576c23a097aa91f5ce897bdd086888acd44034d578a88b7827ea2\" alt=\"9 equals, v squared\"></span>. Taking the square root of both sides yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2d3924ca5c69b120218a22d7f9193aed8741b132e75c8ae3f79e024057fa0604\" alt=\"v equals, negative 3\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cd72302e18507108b8a389d7d9473f3ff7d471f1b8e8ef8a9420236c784cf3e5\" alt=\"v equals 3\"></span>. Since speed can’t be expressed as a negative number, the speed of the object is 3 meters per second.</p><p>Choice B is incorrect and may result from computation errors. Choice C is incorrect. This is the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/92e6640425ec2c0cbb58b322909c954a5a6744756df99e8f39789568801c31c7\" alt=\"v squared  \"></span> rather than <span class=\"italic\">v</span>. Choice D is incorrect. This is the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b7fdb3ad7c9e2f0262d837a455d580c3b472b95e383c6e951974e885c4e7f3d7\" alt=\"4 v squared  \"></span> rather than <span class=\"italic\">v</span>.</p><p>&nbsp;</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.628000+00:00","source_updated_at":"2023-08-02T20:25:59.628000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">3</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">6</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">9</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">36</p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}