// Numbas version: exam_results_page_options
{"name": "Using a speed and acceleration graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [{"variables": ["a1", "b1", "c1", "d1", "z1", "f1"], "name": "speeds"}, {"variables": ["mab", "mbc", "mcd", "mde", "mef"], "name": "acceleration"}], "preamble": {"js": "", "css": ""}, "type": "question", "name": "Using a speed and acceleration graph", "parts": [{"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "dropdownlist", "shuffleChoices": false, "showFeedbackIcon": true, "displayColumns": 0, "matrix": [0, "1"], "choices": ["<p>speed</p>", "<p>acceleration</p>"], "scripts": {}, "variableReplacements": [], "marks": 0}, {"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "dropdownlist", "shuffleChoices": false, "showFeedbackIcon": true, "displayColumns": 0, "matrix": ["1", "0"], "choices": ["<p>speed</p>", "<p>acceleration</p>"], "scripts": {}, "variableReplacements": [], "marks": 0}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>The green line with diamond shaped points maps the &nbsp;[[0]]&nbsp;of the car whilst the blue line with circular points maps the&nbsp;[[1]] of the car.</p>"}, {"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "shuffleChoices": false, "showFeedbackIcon": true, "displayColumns": 0, "matrix": [0, "1"], "choices": ["<p>Yes - a car could have a negative speed.</p>", "<p>No - a car can never have a negative speed.</p>"], "scripts": {}, "variableReplacements": [], "marks": 0}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>The graph shows no negative speeds; is there ever a case where the car could've had a negative speed? &nbsp;[[0]]</p>"}, {"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "shuffleChoices": false, "showFeedbackIcon": true, "displayColumns": 0, "matrix": ["1", "0"], "choices": ["<p>Yes - a car could have a negative acceleration.</p>", "<p>No - a car can never have a negative acceleration.</p>"], "scripts": {}, "variableReplacements": [], "marks": 0}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>The graph shows some negative accelerations; is it possible for a car to have negative acceleration? &nbsp;[[0]]</p>"}, {"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"checkingtype": "absdiff", "type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1], "showpreview": true, "answer": "{mab}", "scripts": {}, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "marks": 1, "checkingaccuracy": 0.001, "variableReplacements": [], "expectedvariablenames": []}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>Calculate acceleration over the first $2$ seconds. Use the acceleration line on the graph to check your answer is correct.</p>\n<p>Acceleration $=$ &nbsp;[[0]] $m\\space/\\space s^2$</p>"}], "advice": "<h4>a)</h4>\n<p>We can analyse the nature of each line to find out which line resembles speed and which resembles acceleration.&nbsp;</p>\n<p></p>\n<p>The speed line should be distinguishable from the acceleration line based on the fact speed is always positive and has a continuous function (a line where the points are joined). This suggests the blue line with circular points represents speed.</p>\n<p>Where as acceleration can often be discontinuous and can be negative where speeds are decreasing. This suggests that the green line with diamond shaped points is the acceleration line.</p>\n<h4>b)</h4>\n<p>Speed is a scalar quantity without direction so speed is positive no matter the direction it travels in. Therefore our answer is \"no- a car can never have a negative speed.\".</p>\n<h4>c)</h4>\n<p>By defintion, when an object is slowing down it has a negative acceleration as the acceleration measures that change in speed. Therefore, our answer is \"yes- a car could have negative acceleration.\".</p>\n<h4>d)</h4>\n<p>To calculate acceleration we use the point at $0$ seconds, with a $0$ m/s speed and the point at $2$ seconds with a $\\var{b1}$ m/s speed and we find the gradient of the line between them. To find the gradient of a straight line we can use:</p>\n<p>\\[ <br/>\\begin{align}<br/>\\text{Gradient } &amp;= \\frac{y_1-y_2}{x_1-x_2}\\\\<br/>&amp;= \\frac{\\var{b1-a1}}{2-0}\\\\<br/>&amp;=\\simplify[fractionNumbers,simplifyFractions,unitDenominator]{{b1-a1}/2} \\text{.}<br/>\\end{align}<br/>\\]</p>\n<p>We can then compare the graph to our this answer in order to check that our calculation is correct and&nbsp;we see that we&nbsp;the same answer as was given.</p>\n<h4></h4>", "tags": ["acceleration", "graphs", "speed and acceleration graph", "taxonomy"], "variables": {"area": {"templateType": "anything", "description": "", "definition": "d2farea+c1*2+b1+c1+b1", "name": "area", "group": "Ungrouped variables"}, "d2farea": {"templateType": "anything", "description": "", "definition": "2*z1+d1+f1", "name": "d2farea", "group": "Ungrouped variables"}, "mab": {"templateType": "anything", "description": "", "definition": "(b1-a1)/2", "name": "mab", "group": "acceleration"}, "b1": {"templateType": "anything", "description": "", "definition": "random(6,8,10)+a1\n", "name": "b1", "group": "speeds"}, "mef": {"templateType": "anything", "description": "", "definition": "(f1-z1)/2", "name": "mef", "group": "acceleration"}, "a1": {"templateType": "anything", "description": "", "definition": "0\n", "name": "a1", "group": "speeds"}, "d1": {"templateType": "anything", "description": "", "definition": "c1", "name": "d1", "group": "speeds"}, "f1": {"templateType": "anything", "description": "", "definition": "2", "name": "f1", "group": "speeds"}, "c1": {"templateType": "anything", "description": "", "definition": "random(8,10,12,14)+b1", "name": "c1", "group": "speeds"}, "mde": {"templateType": "anything", "description": "", "definition": "(z1-d1)/2", "name": "mde", "group": "acceleration"}, "mbc": {"templateType": "anything", "description": "", "definition": "(c1-b1)/2", "name": "mbc", "group": "acceleration"}, "mcd": {"templateType": "anything", "description": "", "definition": "(d1-c1)/2", "name": "mcd", "group": "acceleration"}, "z1": {"templateType": "anything", "description": "", "definition": "c1-random(8,10,12)", "name": "z1", "group": "speeds"}}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "functions": {}, "ungrouped_variables": ["d2farea", "area"], "statement": "<p>You are part of a team analysing a high speed car&nbsp;race. You are given the following graph mapping both the speed and acceleration of one particular car&nbsp;as it drives around a section of the race course. The horizontal axis plots time in seconds&nbsp;whilst the vertical axis maps speed and acceleration in metres per second and metres per second squared respectively.</p>\n<p style=\"text-align: center;\">{geogebra_applet('qEUWCdWt',[[\"a1\",a1],[\"b1\",b1],[\"c1\",c1],[\"d1\",d1],[\"z1\",z1],[\"f1\",f1]])}&nbsp;</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.</p>"}, "extensions": ["geogebra"], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}]}