// Numbas version: finer_feedback_settings
{"name": "SUVAT equations question 6", "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", "t"], "name": "SUVAT equations question 6", "tags": [], "advice": "<p>a) We are given $a=\\var{a}, u=\\var{u}$ and $t=\\var{t}$. We are asked to find the distance, $s \\mathrm{m}$ therefore we can use the formula $s=ut+\\frac{1}{2}at^2.$</p>\n<p>\\begin{align} s &amp;= ut+\\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; &amp;= \\var{u}\\times\\var{t} + \\frac{1}{2} \\times \\var{a} \\times \\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; &amp;=\\var[fractionNumbers]{u*t+0.5*a*t^2} \\mathrm{m}. \\end{align}<br/>So the total distance the particle has travelled is $\\var[fractionNumbers]{u*t+0.5*a*t^2} \\mathrm{m}.$</p>\n<p>b) It is a good idea to use data given in the question, therefore to find $v$ we will use the formula $v=u+at$.</p>\n<p>\\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;&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; &amp;= \\var[fractionNumbers]{u+a*t} \\mathrm{ms^{-1}}. \\end{align}</p>\n<p>The particle is travelling at $\\var[fractionNumbers]{u+a*t} \\mathrm{ms^{-1}}$ when it passes point $X$.</p>", "rulesets": {}, "parts": [{"prompt": "<p>What is the total distance in $\\mathrm{m}$ the particle has travelled when it reaches point $X$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "u*t+0.5*a*t^2", "minValue": "u*t+0.5*a*t^2", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "<p>At what speed in $\\mathrm{ms^{-1}}$ does the particle pass point $X$?</p>", "allowFractions": true, "variableReplacements": [], "maxValue": "u+a*t", "minValue": "u+a*t", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "extensions": [], "statement": "<p>A particle is moving alone a straight line with constant acceleration of $\\var{a} \\mathrm{ms^{-2}}$. Initially the particle travels at $\\var{u}\\mathrm{ms^{-1}}$, then $\\var{t}$ seconds later it hits a point $X$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(1..5#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": "<p>acceleration</p>"}, "u": {"definition": "random(1..6#0.5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "u", "description": "<p>initial velocity</p>"}, "t": {"definition": "random(5..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "t", "description": "<p>time taken</p>"}}, "metadata": {"description": "<p>uses $s=ut+\\frac{1}{2}at^2$</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/"}]}