// 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}, "question_groups": [{"questions": [{"functions": {}, "type": "question", "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "

You are part of a team analysing a high speed car race. You are given the following graph mapping both the speed and acceleration of one particular car as it drives around a section of the race course. The horizontal axis plots time in seconds whilst the vertical axis maps speed and acceleration in metres per second and metres per second squared respectively.

\n

{geogebra_applet('qEUWCdWt',[[\"a1\",a1],[\"b1\",b1],[\"c1\",c1],[\"d1\",d1],[\"z1\",z1],[\"f1\",f1]])}

#### a)

\n

We can analyse the nature of each line to find out which line resembles speed and which resembles acceleration.

\n

\n

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.

\n

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.

\n

#### b)

\n

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.\".

\n

#### c)

\n

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.\".

\n

#### d)

\n

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:

\n

\\\begin{align} \\text{Gradient } &= \\frac{y_1-y_2}{x_1-x_2}\\\\ &= \\frac{\\var{b1-a1}}{2-0}\\\\ &=\\simplify[fractionNumbers,simplifyFractions,unitDenominator]{{b1-a1}/2} \\text{.} \\end{align} \

\n

We can then compare the graph to our this answer in order to check that our calculation is correct and we see that we the same answer as was given.

\n", "ungrouped_variables": ["d2farea", "area"], "variables": {"mab": {"definition": "(b1-a1)/2", "group": "acceleration", "description": "", "name": "mab", "templateType": "anything"}, "mef": {"definition": "(f1-z1)/2", "group": "acceleration", "description": "", "name": "mef", "templateType": "anything"}, "d2farea": {"definition": "2*z1+d1+f1", "group": "Ungrouped variables", "description": "", "name": "d2farea", "templateType": "anything"}, "a1": {"definition": "0\n", "group": "speeds", "description": "", "name": "a1", "templateType": "anything"}, "mde": {"definition": "(z1-d1)/2", "group": "acceleration", "description": "", "name": "mde", "templateType": "anything"}, "mcd": {"definition": "(d1-c1)/2", "group": "acceleration", "description": "", "name": "mcd", "templateType": "anything"}, "area": {"definition": "d2farea+c1*2+b1+c1+b1", "group": "Ungrouped variables", "description": "", "name": "area", "templateType": "anything"}, "c1": {"definition": "random(8,10,12,14)+b1", "group": "speeds", "description": "", "name": "c1", "templateType": "anything"}, "z1": {"definition": "c1-random(8,10,12)", "group": "speeds", "description": "", "name": "z1", "templateType": "anything"}, "f1": {"definition": "2", "group": "speeds", "description": "", "name": "f1", "templateType": "anything"}, "b1": {"definition": "random(6,8,10)+a1\n", "group": "speeds", "description": "", "name": "b1", "templateType": "anything"}, "d1": {"definition": "c1", "group": "speeds", "description": "", "name": "d1", "templateType": "anything"}, "mbc": {"definition": "(c1-b1)/2", "group": "acceleration", "description": "", "name": "mbc", "templateType": "anything"}}, "rulesets": {}, "parts": [{"type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "gaps": [{"type": "1_n_2", "displayColumns": 0, "showFeedbackIcon": true, "variableReplacements": [], "customMarkingAlgorithm": "", "matrix": [0, "1"], "shuffleChoices": false, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "showCellAnswerState": true, "variableReplacementStrategy": "originalfirst", "choices": ["

speed

", "

acceleration

"], "maxMarks": 0, "scripts": {}, "distractors": ["", ""], "minMarks": 0, "unitTests": [], "displayType": "dropdownlist", "marks": 0}, {"type": "1_n_2", "displayColumns": 0, "showFeedbackIcon": true, "variableReplacements": [], "customMarkingAlgorithm": "", "matrix": ["1", "0"], "shuffleChoices": false, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "showCellAnswerState": true, "variableReplacementStrategy": "originalfirst", "choices": ["

speed

", "

acceleration

"], "maxMarks": 0, "scripts": {}, "distractors": ["", ""], "minMarks": 0, "unitTests": [], "displayType": "dropdownlist", "marks": 0}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

The green line with diamond shaped points maps the  [[0]] of the car whilst the blue line with circular points maps the [[1]] of the car.

", "sortAnswers": false, "marks": 0}, {"type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "gaps": [{"type": "1_n_2", "displayColumns": 0, "showFeedbackIcon": true, "variableReplacements": [], "customMarkingAlgorithm": "", "matrix": [0, "1"], "shuffleChoices": false, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "showCellAnswerState": true, "variableReplacementStrategy": "originalfirst", "choices": ["

Yes - a car could have a negative speed.

", "

No - a car can never have a negative speed.

"], "maxMarks": 0, "scripts": {}, "distractors": ["", ""], "minMarks": 0, "unitTests": [], "displayType": "radiogroup", "marks": 0}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

The graph shows no negative speeds; is there ever a case where the car could've had a negative speed?  [[0]]

", "sortAnswers": false, "marks": 0}, {"type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "gaps": [{"type": "1_n_2", "displayColumns": 0, "showFeedbackIcon": true, "variableReplacements": [], "customMarkingAlgorithm": "", "matrix": ["1", "0"], "shuffleChoices": false, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "showCellAnswerState": true, "variableReplacementStrategy": "originalfirst", "choices": ["

Yes - a car could have a negative acceleration.

", "

No - a car can never have a negative acceleration.

"], "maxMarks": 0, "scripts": {}, "distractors": ["", ""], "minMarks": 0, "unitTests": [], "displayType": "radiogroup", "marks": 0}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

The graph shows some negative accelerations; is it possible for a car to have negative acceleration?  [[0]]

", "sortAnswers": false, "marks": 0}, {"type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "gaps": [{"type": "jme", "showPreview": true, "showFeedbackIcon": true, "expectedVariableNames": [], "checkVariableNames": false, "vsetRangePoints": 5, "checkingType": "absdiff", "answer": "{mab}", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "vsetRange": [0, 1], "scripts": {}, "checkingAccuracy": 0.001, "failureRate": 1, "extendBaseMarkingAlgorithm": true, "unitTests": [], "variableReplacements": [], "customMarkingAlgorithm": "", "marks": "1"}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "

Calculate acceleration over the first 2 seconds. Use the acceleration line on the graph to check your answer is correct.

\n

Acceleration $=$  [[0]] m/s$^2$

", "sortAnswers": false, "marks": 0}], "variable_groups": [{"variables": ["a1", "b1", "c1", "d1", "z1", "f1"], "name": "speeds"}, {"variables": ["mab", "mbc", "mcd", "mde", "mef"], "name": "acceleration"}], "name": "Using a speed and acceleration graph", "extensions": ["geogebra"], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}], "tags": [], "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

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.

"}}], "pickingStrategy": "all-ordered"}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}]}