// Numbas version: exam_results_page_options
{"name": "David's copy of Using compound units - speed", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"scripts": {}, "prompt": "<p><em></em>What was the runner's average speed, in metres per second?</p>\n<p>[[0]] m/s</p>\n<p><em></em></p>", "showFeedbackIcon": true, "gaps": [{"showPrecisionHint": false, "correctAnswerStyle": "plain", "precisionMessage": "<p>Round your answer to $2$ decimal places.</p>", "showFeedbackIcon": true, "minValue": "distance/seconds", "precisionType": "dp", "type": "numberentry", "strictPrecision": false, "maxValue": "distance/seconds", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "precision": "2", "mustBeReducedPC": 0, "scripts": {}, "mustBeReduced": false, "precisionPartialCredit": 0, "showCorrectAnswer": true, "correctAnswerFraction": false, "marks": 1, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"]}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"scripts": {}, "prompt": "<p>How fast is this in kilometres per hour?</p>\n<p>[[0]] km/h</p>", "showFeedbackIcon": true, "gaps": [{"showPrecisionHint": false, "correctAnswerStyle": "plain", "precisionMessage": "<p>Round your answer to $2$ decimal places.</p>", "showFeedbackIcon": true, "minValue": "distance/seconds*3.6", "precisionType": "dp", "type": "numberentry", "strictPrecision": false, "maxValue": "distance/seconds*3.6", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "precision": "2", "mustBeReducedPC": 0, "scripts": {}, "mustBeReduced": false, "precisionPartialCredit": 0, "showCorrectAnswer": true, "correctAnswerFraction": false, "marks": 1, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"]}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}], "tags": ["taxonomy"], "advice": "<h4>a)</h4>\n<p>To find the average speed of the runner in meters per second (m/s), we divide the distance covered by the runner (in metres) by the time taken for the runner to run this distance (in seconds).</p>\n<p>\\[<br/>\\begin{align}<br/>\\text{Average speed} &amp;= \\displaystyle\\frac{\\var{distance}}{\\var{seconds}}\\\\<br/>&amp;= \\var{distance/seconds}\\\\<br/>&amp;= \\var{dpformat(distance/seconds,2)}\\; \\text{m/s} \\; (\\text{rounded to $2$ decimal places}).<br/>\\end{align}<br/>\\]</p>\n<h4>b)</h4>\n<p>We can convert the average speed of the runner that we calculated in <strong>a) </strong>in metres per second to kilometres per hour using the following two equivalences:</p>\n<p>\\[1\\text{m} = \\displaystyle\\frac{1}{1000}\\text{km},\\]</p>\n<p>\\[<br/>1 \\; \\text{second} = \\displaystyle\\frac{1}{60} \\; \\text{minutes} = \\displaystyle\\frac{1}{3600} \\; \\text{hours}.<br/>\\]</p>\n<p>We know from <strong>a) </strong>that the average speed of the runner in m/s was $\\var{dpformat(distance/seconds,5)}$ m/s ($5$ d.p), so to convert this speed to km/h we first need to convert metres to kilometres,</p>\n<p>\\[\\var{dpformat(distance/seconds,5)} \\; \\text{m/s} = \\var{dpformat(distance/seconds/1000,5)} \\text{km/s} \\; (5 \\; \\text{d.p})\\]</p>\n<p>Then we convert seconds to hours,</p>\n<p>\\[1 \\; \\text{second} = \\displaystyle\\frac{1}{3600} \\; \\text{hours}.\\]</p>\n<p>Now we have</p>\n<p>\\[\\var{dpformat(distance/seconds,5)} \\; \\text{m/s} = \\var{sigformat(distance/seconds/1000,5)} \\; \\text{kilometres per $\\displaystyle\\frac{1}{3600}$ hours}.\\]</p>\n<p>We want a rate per <strong>one </strong>hour, so we multiply by $3600$ to obtain a measurement in km/h:</p>\n<p><span data-jme-visible=\"(distance/seconds*3.6) &lt;&gt; precround((distance/seconds*3.6),2)\">\\[\\begin{align}\\var{sigformat(distance/seconds/1000,5)} \\; \\text{kilometres per $\\displaystyle\\frac{1}{3600}$ hours} &amp;= \\var{siground(distance/seconds/1000,5)*3600} \\; \\text{km}/\\text{h}\\\\&amp;=\\var{dpformat(distance/seconds*3.6, 2)} \\; \\text{km}/\\text{h} \\; (\\text{rounded to $2$ decimal places}).\\end{align}\\]</span></p>\n<p><span data-jme-visible=\"(distance/seconds*3.6) = precround((distance/seconds*3.6),2)\">\\[\\var{sigformat(distance/seconds/1000,5)} \\; \\text{kilometres per $\\displaystyle\\frac{1}{3600}$ hours} = \\var{distance/seconds*3.6} \\; \\text{km}/\\text{h}.\\]</span></p>\n<p>Note that throughout this calculation we have rounded all figures to $5$ decimal places for convenience; when doing calculations which involve long decimals, you should always input the full figure into your calculator to avoid getting an incorrect answer due to rounding.</p>", "statement": "<p>An athlete&nbsp;runs $\\var{distance}$ m in $\\var{seconds}$ seconds.</p>\n<p><em>Round each of your answers to two decimal places.</em></p>", "variablesTest": {"condition": "", "maxRuns": "100"}, "functions": {}, "variables": {"seconds": {"templateType": "anything", "definition": "floor(distance/speed)", "name": "seconds", "group": "Ungrouped variables", "description": "<p>Time taken to cover the distance, in seconds.</p>"}, "distance": {"templateType": "anything", "definition": "random(80,100,150,200)", "name": "distance", "group": "Ungrouped variables", "description": "<p>Distance that the runner ran.</p>"}, "speed": {"templateType": "anything", "definition": "random(4..8#0)", "name": "speed", "group": "Ungrouped variables", "description": "<p>Athlete's speed, in m/s.</p>\n<p>4m/s is about 9 mph, a bit faster than a jog. The current world record is 12m/s.</p>"}}, "ungrouped_variables": ["distance", "seconds", "speed"], "extensions": [], "variable_groups": [], "rulesets": {}, "name": "David's copy of Using compound units - speed", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Calculate a speed in m/s given distance and time taken, then convert that to km/hour</p>"}, "preamble": {"css": "", "js": ""}, "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}]}