Drawing Velocity Time Graphs from Position Time Graphs

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Drawing Velocity Time Graphs from Position Time
Graphs

• Uniform and Non-Uniform Motion

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Think about

• Sketch a position-time graph of each object
  listed below. Describe its slope as positive or
  negative, and as constant, increasing, or
  decreasing.
• A) a stone at rest
• B) a jogger moving steadily to the right
• C) a bicycle moving to the left and slowing down
• D) a rocket moving up at an increasing speed
• E) a stone falling freely with increasing speed
• F) a parachutist drifting down at a steady speed

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Non-Uniform Motion

• An object does not always move at a constant
  speed.
• You may speed up or slow down.
• Non-uniform motion, when graphed, appears as a
  curve not a straight line.

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Instantaneous Velocity

• When you are driving on the highway and you look
  down at your speedometer, you are traveling at
  55 km/h. At that instant in time, 55 km/h is
  your instantaneous velocity.
• For uniform motion, your instantaneous velocity
  is the same as you average velocity.
• For non-uniform motion, your instantaneous
  velocity changes.

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Finding Instantaneous Velocity from a Graph
(Uniform Motion)

• To find instantaneous velocity on a uniform
  position-time graph, just find the average
  velocity for the given segment.

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Finding Instantaneous Velocity from a Graph
(Non-Uniform Motion)

• To find instantaneous velocity on a non-uniform
  position-time graph, draw a line that is tangent
  to the curve at that point.
• The slope is the instantaneous velocity (take the
  two points on the tangent from each side of the
  point).

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http//en.wikipedia.org/wiki/Tangent
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Instantaneous Velocity (Non-uniform Motion)
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Worksheet
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What does a v-t graph look like?

• Time is marked on the horizontal axis and
  velocity is on the vertical.
• Graphs that represent an objects velocity versus
  its time.

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What can we determine from a velocity time graph?

• Velocity and speed
• Time
• Acceleration
• Displacement and distance

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What can we determine from a velocity time graph?

• Velocity - reading directly off the y-axis

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What can we determine from a velocity time graph?

• Time (read off the x-axis)

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What can we determine from a velocity time graph?

• Displacement area under the curve
• NOTE Area formulas
• Arearectangle length x width
• Areatriangle ½ base x height

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What can we determine from a velocity time graph?

• Acceleration v/t slope

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What can you find from a v-t graph

• Acceleration slope at a point on the graph (you
  may have to use a tangent)
• Average acceleration finding the slope of a
  segment (use the start and end points)

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Interpreting v-t graphs

• Horizontal lines show uniform motion (constant
  speed and direction).
• Inclined lines show change in speed or direction,
  or both in other words accelerated motion.

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Velocity-Time Graphs
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Worksheet
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• How can we use d-t graphs to determine v-t
  graphs?
• Find the velocity for each section of the graph
  and plot it (make a list of points).

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Page 57

• Page 57, question 4
• Page 58, question 5
• Worksheet