// Numbas version: exam_results_page_options {"name": "Using compound units - speed", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "preamble": {"js": "", "css": ""}, "type": "question", "name": "Using compound units - speed", "parts": [{"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "variableReplacements": [], "precisionMessage": "
Round your answer to $2$ decimal places.
", "precisionType": "dp", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "allowFractions": false, "showPrecisionHint": false, "strictPrecision": false, "maxValue": "distance/seconds", "precision": "2", "marks": 1, "scripts": {}, "minValue": "distance/seconds", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"]}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "What was the runner's average speed, in metres per second?
\n[[0]] m/s
\n"}, {"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"correctAnswerFraction": false, "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "variableReplacements": [], "precisionMessage": "
Round your answer to $2$ decimal places.
", "precisionType": "dp", "mustBeReducedPC": 0, "precisionPartialCredit": 0, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "allowFractions": false, "showPrecisionHint": false, "strictPrecision": false, "maxValue": "distance/seconds*3.6", "precision": "2", "marks": 1, "scripts": {}, "minValue": "distance/seconds*3.6", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"]}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "How fast is this in kilometres per hour?
\n[[0]] km/h
"}], "advice": "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).
\n\\[
\\begin{align}
\\text{Average speed} &= \\displaystyle\\frac{\\var{distance}}{\\var{seconds}}\\\\
&= \\var{distance/seconds}\\\\
&= \\var{dpformat(distance/seconds,2)}\\; \\text{m/s} \\; (\\text{rounded to $2$ decimal places}).
\\end{align}
\\]
We can convert the average speed of the runner that we calculated in a) in metres per second to kilometres per hour using the following two equivalences:
\n\\[1\\text{m} = \\displaystyle\\frac{1}{1000}\\text{km},\\]
\n\\[
1 \\; \\text{second} = \\displaystyle\\frac{1}{60} \\; \\text{minutes} = \\displaystyle\\frac{1}{3600} \\; \\text{hours}.
\\]
We know from a) 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,
\n\\[\\var{dpformat(distance/seconds,5)} \\; \\text{m/s} = \\var{dpformat(distance/seconds/1000,5)} \\text{km/s} \\; (5 \\; \\text{d.p})\\]
\nThen we convert seconds to hours,
\n\\[1 \\; \\text{second} = \\displaystyle\\frac{1}{3600} \\; \\text{hours}.\\]
\nNow we have
\n\\[\\var{dpformat(distance/seconds,5)} \\; \\text{m/s} = \\var{sigformat(distance/seconds/1000,5)} \\; \\text{kilometres per $\\displaystyle\\frac{1}{3600}$ hours}.\\]
\nWe want a rate per one hour, so we multiply by $3600$ to obtain a measurement in km/h:
\n\\[\\begin{align}\\var{sigformat(distance/seconds/1000,5)} \\; \\text{kilometres per $\\displaystyle\\frac{1}{3600}$ hours} &= \\var{siground(distance/seconds/1000,5)*3600} \\; \\text{km}/\\text{h}\\\\&=\\var{dpformat(distance/seconds*3.6, 2)} \\; \\text{km}/\\text{h} \\; (\\text{rounded to $2$ decimal places}).\\end{align}\\]
\n\\[\\var{sigformat(distance/seconds/1000,5)} \\; \\text{kilometres per $\\displaystyle\\frac{1}{3600}$ hours} = \\var{distance/seconds*3.6} \\; \\text{km}/\\text{h}.\\]
\nNote 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.
", "tags": ["taxonomy"], "variables": {"speed": {"templateType": "anything", "description": "Athlete's speed, in m/s.
\n4m/s is about 9 mph, a bit faster than a jog. The current world record is 12m/s.
", "definition": "random(4..8#0)", "name": "speed", "group": "Ungrouped variables"}, "distance": {"templateType": "anything", "description": "Distance that the runner ran.
", "definition": "random(80,100,150,200)", "name": "distance", "group": "Ungrouped variables"}, "seconds": {"templateType": "anything", "description": "Time taken to cover the distance, in seconds.
", "definition": "floor(distance/speed)", "name": "seconds", "group": "Ungrouped variables"}}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": "100"}, "functions": {}, "ungrouped_variables": ["distance", "seconds", "speed"], "statement": "An athlete runs $\\var{distance}$ m in $\\var{seconds}$ seconds.
\nRound each of your answers to two decimal places.
", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Calculate a speed in m/s given distance and time taken, then convert that to km/hour
"}, "extensions": [], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}