// Numbas version: exam_results_page_options
{"name": "Simon's copy of SUVAT equations question 4", "extensions": [], "custom_part_types": [], "resources": [["question-resources/man_image.png", "/srv/numbas/media/question-resources/man_image.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "<p>A pedestrian waits at a crossing until the&nbsp;road is clear. He crosses the road with constant acceleration, starting from rest and $\\var{t}$ seconds later he&nbsp;passes a shop and is&nbsp;travelling at $\\var{km} \\mathrm{km \\ h^{-1}}.$&nbsp;</p>\n<p><img width=\"327\" height=\"120\" style=\"margin-right: auto; margin-left: auto; display: block;\" src=\"resources/question-resources/man_image.png\"/></p>\n<p></p>", "variables": {"t": {"name": "t", "definition": "random(20..60#1)", "description": "<p>time he passes the shop</p>", "templateType": "randrange", "group": "Ungrouped variables"}, "km": {"name": "km", "definition": "random(1..8#1)", "description": "<p>pedestrains speed in km. students convert to metres.</p>", "templateType": "randrange", "group": "Ungrouped variables"}}, "ungrouped_variables": ["t", "km"], "extensions": [], "parts": [{"prompt": "<p>Convert $\\var{km} \\mathrm{km \\ h^{-1}}$ into SI units $\\mathrm{ms^{-1}}$ (enter your answer as a fraction).</p>", "allowFractions": true, "type": "numberentry", "minValue": "km*1000/3600", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "correctAnswerStyle": "plain", "unitTests": [], "showCorrectAnswer": true, "mustBeReducedPC": 0, "marks": 1, "extendBaseMarkingAlgorithm": true, "maxValue": "km*1000/3600", "scripts": {}, "correctAnswerFraction": true, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>What is the pedestrian's acceleration in $\\mathrm{ms^{-2}}$?</p>", "allowFractions": true, "type": "numberentry", "minValue": "(km*1000/3600)/t", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "correctAnswerStyle": "plain", "unitTests": [], "showCorrectAnswer": true, "mustBeReducedPC": 0, "marks": 1, "extendBaseMarkingAlgorithm": true, "maxValue": "(km*1000/3600)/t", "scripts": {}, "correctAnswerFraction": true, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Find the distance in $\\mathrm{m}$ from the crossing to the shop.</p>", "allowFractions": true, "type": "numberentry", "minValue": "(km*1000/3600)*0.5*t", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "correctAnswerStyle": "plain", "unitTests": [], "showCorrectAnswer": true, "mustBeReducedPC": 0, "marks": 1, "extendBaseMarkingAlgorithm": true, "maxValue": "(km*1000/3600)*0.5*t", "scripts": {}, "correctAnswerFraction": true, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst"}], "preamble": {"css": "", "js": ""}, "name": "Simon's copy of SUVAT equations question 4", "tags": [], "rulesets": {}, "advice": "<p>a) It is important to always convert your measurements to base SI units before using the SUVAT equations. For velocity, the SI units are $\\mathrm{ms^{-1}}$. We have $\\mathrm{km \\ h^{-1}}$, where $1\\mathrm{km} = 1000\\mathrm{m}$ and $1\\mathrm{h} = 60 \\times 60 \\mathrm{s} = 3600\\mathrm{s}$.</p>\n<p>Therefore</p>\n<p>&nbsp;\\begin{align} \\var{km} \\mathrm{km \\ h^{-1}} &amp; = \\var{km} \\times 1000&nbsp;\\div 3600 \\mathrm{ms^{-1}},\\\\&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &amp; = \\var[fractionNumbers]{km*1000/3600}\\mathrm{ms^{-1}}. \\end{align}&nbsp;&nbsp;</p>\n<p>b) &nbsp;As the pedestrian starts from rest $u=0$. Then we have $v=\\var[fractionNumbers]{km*1000/3600}$, $t=\\var{t}$, $a=?$ and $s=?$. We want $a$ so we can use $v=u+at$ rearranged for $a$, remembering to use our $v$ in SI units from part a).</p>\n<p>\\begin{align} a &amp;= \\frac{v-u}{t}, \\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&amp;= \\frac{\\var[fractionNumbers]{km*1000/3600} - 0}{\\var{t}}, \\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &amp;= \\var[fractionNumbers]{(km*1000/3600)/t} \\mathrm{ms^{-2}}. \\end{align}</p>\n<p>The acceleration of the pedestrian is $\\var[fractionNumbers]{(km*1000/3600)/t} \\mathrm{ms^{-2}}.$</p>\n<p>c) We want the distance, $s$. So we use $s = \\left(\\frac{u+v}{2}\\right)t$.</p>\n<p>\\begin{align} s &amp; = &nbsp;\\left(\\frac{u+v}{2}\\right)t, \\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&amp; = &nbsp;\\left(\\frac{0+\\var[fractionNumbers]{km*1000/3600}}{2}\\right)\\times \\var{t}, \\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &amp; = \\var[fractionNumbers]{(km*1000/3600)*0.5*t} \\mathrm{m}.\\end{align}</p>\n<p>The distance between the crossing and the shop is $\\var[fractionNumbers]{(km*1000/3600)*0.5*t}\\mathrm{m}.$</p>\n<p>&nbsp;</p>", "variable_groups": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}