// Numbas version: exam_results_page_options {"name": "Q1 Constant Acceleration", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Q1.png", "/srv/numbas/media/question-resources/Q1.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["s", "u", "v", "a", "t", "v1", "s1"], "name": "Q1 Constant Acceleration", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

(a)	\n $u = \\var{u}; v = \\var{v}; s = \\var{s}; t = \\,?$ \n

	\n Using $s = \\frac{1}{2}(u+v)t\\,\\,$ and rearranging for $t$ gives \n

	\n $t = \\frac{2 \\times s}{u+v} = \\frac{2 \\times \\var{s}}{\\var{u}+\\var{v}} = \\var{precround(t,3)}\\,$ seconds \n

(b)	\n Find the acceleration of the car using $v = u + at$ \n

	$a = \\frac{v-u}{t} = \\frac{\\var{v}-\\var{u}}{\\var{precround(t,3)}} = \\var{precround(a,3)}\\,ms^{-2}$



	\n Then for the car travelling from A to M, we have \n
	\n $u = \\var{u}; v = \\,?; a = \\var{precround(a,3)}; s = \\var{precround(s1,2)}$ \n

	\n Using $v^{2} = u^{2}+2as$ gives \n

	\n $v^{2} = (\\var{u})^{2}+(2 \\times \\var{precround(a,3)} \\times \\var{s})$ \n

	\n $v = \\var{precround(v1,3)}\\,ms^{-1}$ \n

", "rulesets": {}, "parts": [{"prompt": "

The time taken by the car to move from A to B = [[0]] seconds

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "sigfig", "precisionMessage": "

You have not given your answer to the correct precision.

", "allowFractions": false, "variableReplacements": [], "maxValue": "t", "strictPrecision": false, "minValue": "t", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": "0", "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

The speed with which the car passes M = [[0]] $ms^{-1}$

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "sigfig", "precisionMessage": "

You have not given your answer to the correct precision.

", "allowFractions": true, "variableReplacements": [], "maxValue": "v1", "strictPrecision": false, "minValue": "v1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "

A car is moving along a straight road with uniform acceleration

The car passes a point A with a speed of $\\var{u}\\,ms^{-1}$ and another point B with a speed of $\\var{v}\\,ms^{-1}$

The distance from A to B is $\\var{s}\\,m$

(a) Find the time taken by the car to move from A to B

M is the mid-point of AB

(b) Find the speed with which the car passes M

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "(v-u)/t", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "s1": {"definition": "s/2\n", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}, "v1": {"definition": "sqrt((u*u)+(2*a*s1))", "templateType": "anything", "group": "Ungrouped variables", "name": "v1", "description": ""}, "s": {"definition": "random(300..800#100)", "templateType": "randrange", "group": "Ungrouped variables", "name": "s", "description": ""}, "u": {"definition": "random(5..25#5)", "templateType": "randrange", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "(2*s)/(u+v)", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "v": {"definition": "random(30..40#2)", "templateType": "randrange", "group": "Ungrouped variables", "name": "v", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Stephen Bowlzer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/206/"}]}]}], "contributors": [{"name": "Stephen Bowlzer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/206/"}]}