Car and Ramp

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Car and Ramp

• Part Four Graphs of Motion

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Learning Goals

• Construct and analyze graphs of position versus
  time, and speed versus time.
• Recognize and explain how the slope of a line
  describes the motion of an object.
• Explain the meaning of constant speed.

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Graphs of Motion

• Constant speed means the speed stays the same.
• An object moving at a constant speed always
  creates a position vs. time graph that is a
  straight line.

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Slope

• The slope of a line is the ratio of the rise
  (vertical change) to the run(horizontal change)
  of the line.

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Position-Time Graph

• A position versus time graph can tell you whether
  an objects speed is constant or changes.
• Remember, if the speed is constant, the graph is
  a straight line with a constant slope.
• But if the speed is changing, the slope changes,
  so the graph curves.

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Position-Time Graph

• Consider the speed of an accelerating ball in
  free fall.
• As time passes, the balls speed increases.
• Because the slope equals the speed, the slope
  must also become greater with time.

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Position-Time Graph

• The position-time graph of an object slowing down
  is also curved.
• A car gradually comes to a stop at a red light.
• As time passes, the cars speed decreases.

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Speed vs. Time Graph for Constant Speed

• The speed versus time graph has speed on the
  y-axis and time on the x-axis.
• On this graph, a constant speed is a straight
  horizontal line.

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Calculating Distance

• A speed versus time graph also can be used to
  find the distance the object has traveled.
• Suppose we draw a rectangle on the speed versus
  time graph between the
• x - axis and the line showing the speed. The area
  of the rectangle (shown below) is equal to its
  length times its height.

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