Physics M1 Graphs II

OBJECTIVESOBJECTIVES GradientGradient x- and y-interceptsx- and y-intercepts QUIZQUIZINTRODUCTIONINTRODUCTION

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Physics Module 1 Unit 1 Lesson 15BEGINBEGIN


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1. Which of the inclined planes in the diagrams do you think has the largest gradient?

2. Give your reason for your response to the question

Feedback: 1: C 2: The slope of the incline is greaest.Click here to check your responses

A B C D

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As a result of this lesson, you will be able to: explain the term gradient; calculate the gradient of a straight line graph using correct

procedure; deduce the units of the gradient of a graph; state what is intercept of a graph; differentiate between an x-intercept and a y-intercept; read off the y-intercept of a graph and state its units.

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1. Which line has greater gradient? Click Line 1 or Line 2 to indicate your response.

Line 1 Line 1Line 1

Line 2

Try again

Observe the red, green and blue arrows on the diagram.

Answer #1: Horizontal distance across

Answer #2: Vertical heights at the same horizontal distance across

Answer #3: Green arrow is for the line of smaller gradient; blue for the line of greater gradient

Click here for answer



1. What does the red arrow represent?

2. What do the green and blue arrows represent?

3. How are the lengths of the green and blue arrows related to the gradients of the lines?

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The gradient of an incline is a measure of the steepness or slope of the inclineThe gradient of an incline is calculated from

gradient = rise / run

Rise

Run

Rise

Run

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1. The run of two inclines is the same. Which incline would have the greater gradient?

2. Two inclines have the same gradient. The rise of one incline is greater than the other, which incline would have the greater run?

The incline with greater rise

The incline with greater rise

Click here for answerClick here for answer

Click here for answerClick here for answer

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In the illustration shown1.How many units is the rise of the line?2.How many units is the run of the line?3.What is the numerical value of the gradient of the line?

Rise:4 units

Run: 5 units

AnswerAnswer

AnswerAnswer

Gradient = rise/run = 4/5 = 0.8AnswerAnswer

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Rise (↕)

Run (↔)gradient(m) =

2 1

2 1

vertical change ( )

horizontal change ( )

y y

x x

−=−

y1

y2

x2 x1

=

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1. Choose two convenient points on the graph line that are well spaced (more than 2/3 the length of the line).

2. Read off the values of y2, y1, x2 and x1.

3. Calculate the gradient using the equation.

y2 = 3

y1 = -3

x2 = 3

x1 = 1

Choose

Read off

Gradient = (y2 – y1)/(x2 – x1)= 3 – (– 3 )/3 – 1 = 6/2=3

Calculate

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To determine the gradient of a graph, quantities with units are divided. It therefore means that gradients have units.

To determine the units of the gradient of a graph, divide the units of the quantity on the y-axis by the units of the quantity on the x-axis.

The unit of the quantity on the y-axis is s2 and the unit of the quantity on the x-axis is m. The unit of gradient is s2/m or s2m-1

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The gradient of the graph in the diagram is positive. How would you describe a straight line graph with a positive gradient?

Answer

A line has a positive gradient if it goes uphill moving from left to right.

CHECK

Type your response in the box below. You need to be in Slide Show to type in the box and edit text.

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The gradient of the graph in the diagram is positive. How would you describe a straight line graph with a positive gradient?

Answer

A line has a positive gradient if it goes downhill moving from left to right.

CHECK

Type your response in the box below. You need to be in Slide Show to type in the box and edit text.

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1. Look at the graph and identify where the graph cuts the y axis. Can we all this point the y-intercept?

AA

Answer: The x-coordinate is always 0.

2. What can we say about the coordinate of x when the graph cuts y-axis?

YES NO Try again

CHECK

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AA

Ans: yes

1. Look at the graph and identify where the graph cuts the x axis. Can we call this point the x-intercept?

Answer: The y-coordinate is always 0.

2. What can we say about the coordinate of y when the graph cuts x-axis?

YES NO Try again

CHECK

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The x-intercept is the point at which the graph crosses the x-axis.

The y-intercept is the point at which where the graph crosses the y-axis.

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The value of the y-intercept is the reading on the y-axis of the graph at the point where the graph crosses the y-axis.

The unit of the y-intercept is the same as the unit of the quantity on the y-axis

The value of the y-intercept on the graph = – 1.8 V

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Are you ready to test yourself? 1.There are five multiple choice items that you are required to do. 2.For each item, click on the letter of the correct response and then click the button ‘NEXT QUESTION’ to continue.3.Click the BEGIN QUIZ button to start the quiz.

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BEGIN QUIZ!BEGIN QUIZ!


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Which of the surfaces that are highlighted in yellow on the shapes has zero gradient?

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A. I A. I

B. IIB. II

C. IIIC. III

D. IVD. IV

I

II

III

IV

FEEDBACKFEEDBACKFEEDBACKFEEDBACK


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A is incorrect: The surface has negative non-zero gradientB is incorrect: The gradient of the surface is infinite.C is incorrect: The gradient of the surface is positive and non-zeroD is correct: Horizontal surfaces and lines have zero gradient.

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I

II

III

IV

NEXT QUESTIONNEXT QUESTIONNEXT QUESTIONNEXT QUESTION


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What is the unit of the gradient of the graph in the illustration?

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A. PaoCA. PaoC

D. Cannot be determined

D. Cannot be determined

C. oCPa-1C. oCPa-1

B. PaoC-1B. PaoC-1



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What is the unit of the gradient of the graph in the illustration?A is incorrect: The unit of the x-axis is multiplied by the unit of the y-axisB is correct: the unit of the y-axis is divided by the unit of the x-axisC is incorrect: the unit of the x-axis is divided by the unit of the y-axisD is incorrect: The unit of the gradient can be determined

22NEXT QUESTIONNEXT QUESTIONNEXT QUESTIONNEXT QUESTION


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Which best gives the value and unit of the y-intercept of the graph in the illustration?

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A. 300 kPaA. 300 kPa

D. 92 oC D. 92 oC

B. 300 oCB. 300 oC

C. 92 kPaC. 92 kPa



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What is the coordinates of y –intercept of the graph?

A is incorrect: The graph line crosses the Y-axis at 92 kPa.B is incorrect: The graph line crosses the Y-axis at 92 kPa.C is correct: The graph line crosses the Y-axis at 92 kPa.D is incorrect: The graph line crosses the Y-axis at 92 kPa.



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What is the gradient of the section of the graph highlighted in red?

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A. – 2.9 ms-2A. – 2.9 ms-2

D. + 2.9 ms-2D. + 2.9 ms-2

C. – 8.2 ms-2C. – 8.2 ms-2

B. – 20 ms-2B. – 20 ms-2



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What is the gradient of the section of the graph highlighted in red?

Gradient = (y2 – y1)/(x2 – x1) = 80 – (– 60)/(5 –

12) = 140/– 7 = – 20 ms-2

A, C and D are incorrect.B is correct

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y2

y1

x1

x2

NEXT QUESTIONNEXT QUESTIONNEXT QUESTIONNEXT QUESTION


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B. IIB. II

D. IVD. IV

C. IIIC. III

A. IA. I

In which of the diagrams are the two points correctly chosen to determine the gradient of the line?

I

II

III

IV



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In which of the diagrams are the two points correctly chosen to determine the gradient of the line?A is correct: The points chosen are on the line and more than 2/3 the length of the graph line apartB is incorrect: The points chosen are on the line but are too closeC is incorrect: Both of points chosen are not on the lineD is incorrect: Both of the points chosen are not on the line


I

II

III

IV


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What is the y-intercept of -x + 2y = 8?

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A. (-1, 0)A. (-1, 0)

D. (-8, 0)D. (-8, 0)

C. (0, 2)C. (0, 2)

B. (0, 4)B. (0, 4)


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You have reached the end of the quiz. If you wish to review this lesson, click on Introduction to start

the review. If you have finished viewing the lesson, click the Close (X)

button.

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http://cgl.microsoft.com/clipgallerylive/default.asp http://www.physics4u.co.uk http://www.neit.wikispaces.com/file/view/Slope+intro.ppt http://www.teachers.henrico.k12.va.us/math/hcpsalgebra2/..

./2-4/2006_2_4.ppt

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Date post:	22-Jul-2015
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Physics M1 Graphs II

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