# Graphical Analysis

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```					Graphical Analysis

Chapter One in Irwin Physics 11
3 Ways to Use a Graph
1.   You can read values off the graph.
2.   You can find slope(s) of the graph.
3.   You can calculate the area between
the curve and the x-axis of the graph.
1.   Choose a value on
the time axis, 4.6s
2.   Look up the point
on the graph at the
chosen time
3.   Look horizontally to
the position axis
Calculating Slope of the Graph
   `

   The slope of a
position-time graph
is the velocity of the
object.
The units are divided as well

Straight d-t graph only!!!    What does that mean?
Calculating Slope from a d-t graph

What does the negative
sign mean?
The Area "under" the Graph

   The area is between
the graph and the x-
axis
   Use the values that
graph (+ve or –ve)
   What is the area
under this graph?
   What are the units?
Curved Graphs
   What kind of motion
is this?
   What would a slope
represent?
   How would you
calculate the slope?
   How would you
calculate the area?
Tangents
Defined to be:
 A straight line that

"just touches" the
curve at that point
 The slope is the

velocity at that exact
moment
 Instantaneous

Velocity
Calculating tangents in a
curved d-t graph
   What's happening?
   Calculate the slopes
of the tangents (in
red) at A, B, and C
   Do the slopes
correspond to the
motion?
Tangent at A
Tangent at B
Tangent at C
   At point C, the slope
is zero, so the
velocity is zero as
well.
   The object is
slowing down from
30 m/s to 12 m/s to
0 m/s
Average Velocities

   The slope of the
straight line from
point A to point B is
the average velocity
   The slope may be
the average slopes
of the tangent at A
and B but not
always
   Why not?
End of Chapter 1
   1.1 – 1.3: pg. 11 # 2- 3, pg. 13 # 1 – 5

   1.4 – 1.5: pg. 15 # 1 – 2, pg. 19 # 1 – 2

   1.6 – 1.7: pg. 23 # 2a, pg. 34 # 39, 40a

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