Physics M1 Graphs II

OBJECTIVESOBJECTIVES GradientGradient x- and y-interceptsx- and y-intercepts QUIZQUIZINTRODUCTIONINTRODUCTION
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1

Physics  Module 1  Unit 1  Lesson 15
BEGINBEGIN

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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 incline
The 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 shown
1.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 s2
m-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. IA. 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 gradient
B is incorrect: The gradient of the
surface is infinite.
C is incorrect: The gradient of the
surface is positive and non-zero
D 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. Pao
CA. Pao
C
D. Cannot be
determined
D. Cannot be
determined
C. o
CPa-1C. o
CPa-1
B. Pao
C-1B. Pao
C-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-axis
B is correct: the unit of the y-axis
is divided by the unit of the x-axis
C is incorrect: the unit of the x-axis
is divided by the unit of the y-axis
D is incorrect: The unit of the
gradient can be determined
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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 o
CD. 92 o
C
B. 300 o
CB. 300 o
C
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
C is correct: The graph line crosses
the Y-axis at 92 kPa.
D is incorrect: The graph line
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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

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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 apart
B is incorrect: The points chosen are on the
line but are too close
C is incorrect: Both of points chosen are
not on the line
D is incorrect: Both of the points chosen
are not on the line
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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.
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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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