// Numbas version: finer_feedback_settings
{"name": "SUVAT equations question 1", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Car_image.jpg", "/srv/numbas/media/question-resources/Car_image.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "u", "t", "v"], "name": "SUVAT equations question 1", "tags": [], "advice": "<p>You start by writing down the values you know and the values you need to find.</p>\n<p>$a = \\var{a},$ $u=\\var{u},$ $t=\\var{t},$ $v=$ $?,$ $s=$ $?$</p>\n<p>a) At $B$ the car will have reached its final velocity, $v \\mathrm{ms^{-1}}$.&nbsp;You need $v$ and you know $u, a$ and $t$ so you can use the equation $v= u +at$. \\begin{align} v &amp;= u + at, \\\\<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; &amp;= \\var{u} + (\\var{a} \\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;&nbsp;&nbsp; &amp;= \\var{u +a*t} \\mathrm{ms^{-1}}. \\end{align}</p>\n<p>The speed of the car at $B$ is $\\var{u + a*t} \\mathrm{ms^{-1}}.$</p>\n<p>b) You need the distance, $s \\mathrm{m}$. You calculated $v$ in the previous&nbsp;part, so you can use the&nbsp;equation $s=\\left(\\frac{u+v}{2}\\right)t.$</p>\n<p>\\begin{align} s &amp;= \\left(\\frac{u+v}{2}\\right)t, &nbsp;\\\\<br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &amp;= \\left(\\frac{\\var{u}+\\var{v}}{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{((u+v)/2)*t} \\mathrm{m}. \\end{align}<br/>The distance from $A$ to $B$ is $\\var{((u+v)/2)*t}$ metres.</p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>", "rulesets": {}, "parts": [{"integerPartialCredit": 0, "prompt": "<p>Find the speed of the car in $\\mathrm{ms^{-1}}$ at $B$.</p>", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "u+a*t", "minValue": "u+a*t", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Find the distance in $\\mathrm{m}$ from $A$ to $B$.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(u+v)*(0.5)*t", "minValue": "(u+v)*(0.5)*t", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p></p>\n<p>A car is&nbsp;driving in a straight line from $A$ to $B$ with constant acceleration $\\var{a} \\mathrm{ms^{-2}}$.</p>\n<p><img width=\"401\" height=\"119\" style=\"margin-right: auto; margin-left: auto; display: block;\" src=\"resources/question-resources/Car_image.jpg\"/>Its speed at $A$ is&nbsp;$\\var{u} \\mathrm{ms^{-1}}$ and it takes $\\var{t}$ seconds to move from $A$ to $B$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(1..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": "<p>constant acceleration</p>"}, "u": {"definition": "random(1..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "u", "description": "<p>initial speed</p>"}, "t": {"definition": "random(1..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "t", "description": "<p>time (seconds)</p>"}, "v": {"definition": "u+a*t", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": "<p>part a) answer. final velocity</p>"}}, "metadata": {"description": "<p>SUVAT equation questions, for mechanics page in wiki. Uses $v=u+at$ and $s=((u+v)/2)t$.</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/"}]}