// Numbas version: finer_feedback_settings
{"name": "SUVAT equations question 9", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["s", "v", "t", "a", "u"], "name": "SUVAT equations question 9", "tags": [], "advice": "<p>a) We have that $t=\\var{t}, s=\\var{s}$ and $v=\\var{v}$. We are asked to find the acceleration of the car, $a$, therefore we can use the formula $s=vt-\\frac{1}{2}at^2$, rearranged for $a$.</p>\n<p>This gives \\begin{align} s &amp;= vt - \\frac{1}{2}at^2, \\\\<br/>&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;\\frac{1}{2}at^2&nbsp;&nbsp;&amp;= vt - s ,\\\\<br/>&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; a &amp; = \\frac{2(vt-s)}{t^2}, \\\\<br/>&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; = \\frac{2(\\var{v} \\times \\var{t}&nbsp;- \\var{s})}{\\var{t}^2}, \\\\<br/>&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{precround((2(v*t-s))/(t^2),3)}\\mathrm{m^{-2}}. \\end{align}&nbsp;</p>\n<p>So the acceleration of the car is $\\var{precround((2(v*t-s))/(t^2),3)} \\mathrm{ms^{-2}}$.</p>\n<p>b) We are asked to find the initial velocity, $u$. We could use the formula $v=u+at$, however it is best to work with the data given in the question in case our answer to part a) is incorrect. Therefore we will use $s=\\left(\\frac{u+v}{2}\\right)t$ rearranged for $u$.</p>\n<p>This gives \\begin{align} s &amp; = \\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;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; u &amp; = \\frac{2s}{t} - v, \\\\<br/>&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; = \\frac{2 \\times \\var{s}}{\\var{t}} - \\var{v}, \\\\<br/>&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{precround((2*s)/t-v,3)} \\mathrm{ms^{-1}}. \\end{align}<br/>The car was travelling at $\\var{precround((2*s)/t-v,3)} \\mathrm{ms^{-1}}$ when it passed the traffic lights.&nbsp;&nbsp;</p>", "rulesets": {}, "parts": [{"precisionType": "dp", "prompt": "<p>Find the acceleration in $\\mathrm{ms^{-2}}$ (to&nbsp;3d.p.)&nbsp;of the car.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "a", "minValue": "a", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "prompt": "<p>Find the speed in $\\mathrm{ms^{-1}}$ (to 3d.p.) with which the car passed the traffic lights.</p>", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "3", "maxValue": "u", "minValue": "u", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>A car is driving along a straight road with constant acceleration. The car first passes a set of traffic lights then $\\var{s} \\mathrm{m}$ later, travelling at $\\var{v} \\mathrm{ms^{-1}}$ it passes a school. The time it takes the car to go from the traffic lights to the school is $\\var{t}$ seconds.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "a>0\n"}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "2*(v*t-s)/t^2", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": "<p>acceleration</p>"}, "s": {"definition": "random(40..55#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "s", "description": "<p>distance</p>"}, "u": {"definition": "(2*s)/t-v", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(6..9#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "t", "description": "<p>time (seconds)</p>"}, "v": {"definition": "random(5..8#0.25)", "templateType": "randrange", "group": "Ungrouped variables", "name": "v", "description": "<p>final velocity</p>"}}, "metadata": {"description": "<p>Example 9 M1 book</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}]}], "contributors": [{"name": "Amy Chadwick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/505/"}]}