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{"name": "Constant Acceleration: Rearranging Equations 3a", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Constant Acceleration: Rearranging Equations 3a", "tags": [], "metadata": {"description": "<p>Rearraning the constant acceleration equation $v^2=u^2+2as$ to make $u$ the subject.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Rearrange the constant acceleration equation \\[ v^2=u^2+2as \\] to make $u$ the subject.</p>", "advice": "<p>If we want to make $u$ the subject of the equation $v^2=u^2+2as$, this can be broken down into steps.&nbsp;</p>\n<p>Firstly, we want to subtract $2as$ from both sides:</p>\n<p>\\[ \\begin{split} &amp;\\,v^2=u^2+2as \\\\\\\\ \\implies &amp;\\,v^2-2as=u^2 \\,.\\end{split} \\]</p>\n<p>Now the right-hand side of the equation is only $u^2$, so by taking the square root of both sides we can obtain an expression for $u$:</p>\n<p>\\[ \\begin{split}v^2-2as=u^2 \\\\\\\\ \\implies \\sqrt{v^2-2as} &amp;\\,=u \\,.\\end{split} \\]</p>\n<p>Therefore, the equation with $u$ as the subject is \\[ u=\\sqrt{v^2-2as} \\,.\\]</p>\n<p></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$u=$[[0]]<br/><br/></p>\n<ul>\n<li><em>If you need to use a square root, type \"sqrt\". For example, $\\sqrt{x+y}=$ \"sqrt(x+y)\"</em></li>\n<li><em>Remember to use a * when multiplying terms together. For example, ab = a*b</em></li>\n</ul>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "sqrt(v^2-2a*s)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "a", "value": ""}, {"name": "s", "value": ""}, {"name": "v", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}