# Graphs by zahen

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```									GRAPHS

1
23 October 2010
What is the importance of
graphs?
 Provides clear, easily interpreted visual
report of an experimental investigation.
 Can show trends and relationships
between physical quantities which are
not always immediately obvious from a
list of figures.

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PHASE 1

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How to draw a graph
 Deciding on what to plot.
 Deciding on orientation of graph.
 Choosing sensible scales for the axes.
 Giving graph a title.
 Labelling axes.
 Plotting points.
 Drawing the ‘best fit’ line.

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   General Rule – Dependent Variable (y –
axis) versus Independent Variable (x-axis)
running the first 9 seconds of a hundred metre (100m) race.
TIME/s            0   1   2    3       4        5   6   7   8   9
DISTANCE/m        0   5   20 29 38 49 60 70 81 92
Which one of these quantities seem to be dependent on the
other?

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   Based on your data, you may need to
orient your graph as landscape or portrait.
   Use your discretion, taking note of the
range of values for each physical
quantity, and the scales you wish to use.

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 Choose scales that you use much of the
graph paper.
 Scales should always be easy to use and
the values of the intermediate lines on
the graph paper easy to calculate.

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‘y against x’ or
‘y-x graph’ or
‘Graph of y against x’

Note: y and x are substitutes for the specific
names of the physical quantities that you
are comparing.
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   LABEL both axes with the PHYSICAL
QUANTITY and with its UNIT e.g.
Distance/m or Time/s.

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   Accurately mark your points (co-
ordinates) with RINGED DOTS or
CROSSES.

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   Determine from the Data table if the line
should pass through the origin.
   Use a transparent ruler and a sharp pencil
to draw the line.
   In the case of a curved graph, do not use a
ruler but draw a smooth curve to show the
trend.
   The line may not pass through all the points,
but your aim should be to have points
scattered symmetrically on both sides of the
line along the line.
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PHASE 2

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Extracting Information from a Graph

 Extrapolating points.
 Finding the gradient of a graph.
 Finding an intercept on a graph.
 Finding the area under a graph.

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 Extrapolation refers to a process used to
find the value of a quantity outside its
tabulated values.
 Once a ‘best-fit line’ is drawn, a number
of points other than the points from the
data table can be found.

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 Draw a large triangle against the straight
line.
 The sides of the triangle represent the
changes: Δy and Δx.
 It helps to select exact scale graduations
giving easy-to-read values on the x-axis
as you will be dividing by the value of Δx.

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   Intercepts are the values obtained where a
graph cuts an axis.
   The reading from the y-axis intercept is the
value of the y-variable when the x-variable
is zero.
   The reading from the x-axis intercept is the
value of the x-variable when the y-variable
is zero.
   WARNING – your axes must begin at the
origin, otherwise where the line cuts will not
be true intercepts.
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 For straight line graphs, divide the area
into rectangles and triangles and find
the area of each.
 For curved graphs count the squares
and estimate parts of squares making up
the equivalent of whole squares.
 When you count squares you must
multiply the no. of squares by the scale
factor for the value of the total area in
correct units.
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Question 1

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Question 1 (continued)

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Question 2

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Question 2 (continued)

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Question 3
Plot a graph of Length/cm against
Depth/cm (your scale should be at least
extend out to 55 cm).

(The data table is on the next slide.)

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Question 3 (continued)
Length/cm               Depth/cm
5.0                    20.8
10.0                   18.5
14.0                   16.7
17.0                   15.2
20.0                   13.8
23.0                   12.5
27.0                   10.6
30.0                    9.3
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Question 4
   Plot a graph of y/cm against x/cm
starting at the y scale at ‘y = 30 cm’.

(The data table is on the next slide.)

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Question 4 (continued)
x/cm                      y/cm
13.0                      73.0
14.5                      53.5
17.0                      45.4
20.0                      42.6
25.0                      43.3
30.0                      46.5
40.0                      54.7

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Avison, J.H., Neeranjan, D. & Henry, D.
(2007). Physics for CSEC. Nelson Thornes
Ltd: Cheltenham/GB.
   graph of displacement against time
   data for the displacement time graph
   graph of velocity against time
   data for the curved velocity against time graph
   y-axis and x-axis intercepts
   question 1 & question 2

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