Graphical Analysis

							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.
      Reading 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
     and read ~70 m
     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
    you've read off the
    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