// Numbas version: exam_results_page_options
{"name": "SUVAT equations question 2", "extensions": [], "custom_part_types": [], "resources": [["question-resources/truck_image.png", "/srv/numbas/media/question-resources/truck_image.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["u", "v", "t"], "name": "SUVAT equations question 2", "tags": [], "advice": "<p>You start by writing down the values you know and the values you need to find.</p>\n<p>$a =$ $?$, $u=\\var{u},$ $t=\\var{t},$ $v=\\var{v},$ $s=$ $?$</p>\n<p>a) You need the distance $s \\mathrm{m}$ and you know $u, v$ and $t$ so you can use the equation $s= \\left(\\frac{u+v}{2}\\right)t$. \\begin{align}&nbsp;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;&nbsp; &amp;=&nbsp;\\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;&nbsp;&nbsp; &amp;=&nbsp;\\var{(u+v)*0.5*t} \\mathrm{m}.\\end{align}</p>\n<p>The distance the truck travels is $\\var{(u+v)*0.5*t}$ metres.</p>\n<p>b) You need the acceleration, $a \\mathrm{ms^{-2}}$, and you know $u$,$v$ and $t$ so you can use the&nbsp;equation $v=u + at$ rearranged for $a$.</p>\n<p>\\begin{align}&nbsp;a &amp;= \\left(\\frac{v-u}{t}\\right), &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{v}-\\var{u}}{\\var{t}}\\right), \\\\<br/>&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{(v-u)}}{\\var{t}} \\mathrm{ms^{-2}}. \\end{align}<br/>The acceleration of the truck is $\\frac{\\var{(v-u)}}{\\var{t}} \\mathrm{ms^{-2}}$.</p>", "rulesets": {}, "parts": [{"prompt": "<p>Find the distance in $\\mathrm{m}$ that the truck travels in these $\\var{t}$ seconds.</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}, {"prompt": "<p>Find the acceleration in $\\mathrm{ms^{-2}}$ of the truck in these $\\var{t}$ seconds.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(v-u)/t", "minValue": "(v-u)/t", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>A&nbsp;truck accelerates along a straight road at a constant rate from a speed of&nbsp;$\\var{u} \\mathrm{ms^{-1}}$ to $\\var{v} \\mathrm{ms^{-1}}$ in $\\var{t}$ seconds.</p>\n<p><img width=\"397\" height=\"134\" style=\"margin-right: auto; margin-left: auto; display: block;\" src=\"resources/question-resources/truck_image.png\"/></p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"u": {"definition": "random(2..6#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "u", "description": "<p>initial velocity</p>"}, "t": {"definition": "random(2..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "t", "description": "<p>time</p>"}, "v": {"definition": "random(7..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "v", "description": "<p>final velocity</p>"}}, "metadata": {"description": "", "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/"}]}