// Numbas version: exam_results_page_options
{"name": "NA5 - Convert Units (m/s and km/h)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "NA5 - Convert Units (m/s and km/h)", "tags": [], "metadata": {"description": "<p>Unit conversion between two compound units.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A Cheetah runs at a speed of {speedkm} kilometres per hour (km/h). What is the Cheetah's speed in metres per second (m/s)?</p>\n<p>Give your ansswer to 2 decimal places where appropriate.</p>", "advice": "<p>There are a number of ways to work out the conversion. Here are a couple of suggestions.</p>\n<p><strong>METHOD 1</strong></p>\n<p>Since there are $1000$m in $1$km we first multiply by $1000$ to get the speed in metres per hour:</p>\n<p>\\begin{equation} 1000*\\var{speedkm} = \\var{step1}\\end{equation}</p>\n<p>Then we divide by $3600$ since that is the number of seconds in an hour to get the speed in metres per second:</p>\n<p>\\begin{equation} \\frac{\\var{step1}}{3600} = \\var{speedms} \\end{equation}</p>\n<p>Finally we round off to 2 decimal places as required, $\\var{roundanswer}$m/s.</p>\n<p><strong>METHOD 2</strong></p>\n<p>We can actually do all of the above in one step of working by using a single conversion factor. Since there are $1000$m in a km and $3600$ seconds in an hour, we can calaculate the conversion factor:</p>\n<p>\\begin{equation} \\frac{3600}{1000} = 3.6 \\end{equation}</p>\n<p>and then simply divide by that conversion factor:</p>\n<p>\\begin{equation} \\frac{\\var{speedkm}}{3.6} = \\var{speedms} \\end{equation}</p>\n<p>finally rounding off as before, $\\var{roundanswer}$m/s.</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Conversions\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"speedkm": {"name": "speedkm", "group": "Ungrouped variables", "definition": "random(70 .. 120#10)", "description": "", "templateType": "randrange", "can_override": false}, "speedms": {"name": "speedms", "group": "Ungrouped variables", "definition": "1000*speedkm/3600", "description": "", "templateType": "anything", "can_override": false}, "step1": {"name": "step1", "group": "Ungrouped variables", "definition": "1000*speedkm", "description": "", "templateType": "anything", "can_override": false}, "roundanswer": {"name": "roundanswer", "group": "Ungrouped variables", "definition": "dpformat(speedms,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["speedkm", "speedms", "step1", "roundanswer"], "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>[[0]]m/s</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "answer", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "speedms", "maxValue": "speedms", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "speedms", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}]}]}], "contributors": [{"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}]}