// Numbas version: finer_feedback_settings
{"name": "SUVAT equations question 5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "u", "v"], "name": "SUVAT equations question 5", "tags": [], "advice": "<p>a) We have that $a=\\var{a}$, $u=\\var{u}$, $v=\\var{v}$. We want to find the distance, $s \\mathrm{m}$. We can use the formula $v^2=u^2+2as$ rearranged for $s$.</p>\n<p>Therefore</p>\n<p>\\begin{align} s &amp; = \\frac{v^2 - u^2}{2a}, \\\\<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{v}^2 - \\var{u}^2}{2\\times \\var{a}}, \\\\<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; = \\var[fractionNumbers]{(v^2 - u^2)/(2*a)} \\mathrm{m}. \\end{align}</p>\n<p>So the distance from $A$ to $B$ is $\\var[fractionNumbers]{(v^2 - u^2)/(2*a)} \\mathrm{m}$.</p>\n<p>b) We have all the variables now except for $t$. To find the time travelled we can use&nbsp;the majority of the&nbsp;SUVAT equations, however it is best to use&nbsp;$v=u+at$ rearranged for $t$ as we are given $v, u$ and $a$ in the question, just incase the $s$ that was calculated previously was incorrect.</p>\n<p>Therefore</p>\n<p>\\begin{align} t &amp;= \\frac{v-u}{a}, \\\\<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}-\\var{u}}{\\var{a}}, \\\\<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]{(v-u)/a} \\mathrm{s}. \\end{align}</p>\n<p>The time taken for the car to travel from $A$ to $B$ is $\\var[fractionNumbers]{(v-u)/a} \\mathrm{s}$.&nbsp;</p>", "rulesets": {}, "parts": [{"prompt": "<p>Find the distance in $\\mathrm{m}$ from $A$ to $B$.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(v^2-u^2)/(2*a)", "minValue": "(v^2-u^2)/(2*a)", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>Find the time taken in seconds to travel from $A$ to $B$.</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "(v-u)/a", "minValue": "(v-u)/a", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>A car is driving alone a straight road from $A$ to $B$ with constant acceleration $\\var{a} \\mathrm{ms^{-2}}$. At point&nbsp;$A$ the car is travelling at $\\var{u} \\mathrm{ms^{-1}}$ in the direction $\\simplify{vec:AB}$. At point $B$ the car is travelling in the same direction with velocity $\\var{v} \\mathrm{ms^{-1}}$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "v>u"}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(1..6#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": "<p>acceleration</p>"}, "u": {"definition": "random(1..5#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "u", "description": "<p>initial velocity at point A</p>"}, "v": {"definition": "random(6..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "v", "description": "<p>final velocity at point B</p>"}}, "metadata": {"description": "<p>Section 2.2 of M1 book. Using v squared formula</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/"}]}