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Representing Motion: Graphing

AP Topic 1.3 Part 1

Beta Kappa

Morris Louis

1961

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Learning Objective

Describe the position, velocity, and acceleration of an object using representations of that object’s motion.

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How can we represent motion?

motion diagrams

figures

graphs

v = vo + at

equations

An object is thrown straight upward with a velocity of 4.5 m/s.

narrative description

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Analyzing Motion Graphs

When looking at a motion graph, there are many things to consider that will help you understand what motion is taking place.

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Analyzing Motion Graphs

Axes labels: What type of motion graph is this?

x vs t?

v vs t?

a vs t?

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Analyzing Motion Graphs

Changes in motion: Are there sections in the graph where the motion is changing?

Each of these sections is a change in motion. How do you know?

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Analyzing Motion Graphs

 

Changes in slope!

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Analyzing Motion Graphs

Positive and negative:

  • Are the y-values positive or negative?
  • Does a line cross the axis x-axis?

Positive y-values

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Negative y-values

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Analyzing Motion Graphs

Area Under the Curve:

How much area is under the curve. This gives you information for some graphs.

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Position vs Time Graphs

What do you see in this graph?

  • Axes: x vs t
  • Changes in motion:
    • 0 s to 10 s: positive slope
    • 10 s to 15 s: zero slope
    • 15 s to 40 s: negative slope
    • 40 s to 55 s: positive slope
  • Crosses x-axis at 30 s

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Position vs Time Graphs

 

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Position vs Time Graphs

What’s happening here?

  • What does slope represent?
  • Is the slope constant?
  • What is happening to the slope in this graph? What does that mean?

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Position vs Time Graphs

What does this line represent?

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Position vs Time Graphs

What is the velocity of the object at t = 30 s?

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What is the position of the object at t = 30 s?

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What would a “v vs t” graph for this “x vs t” graph look like?

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Position vs Time Graph Summary

  • + y-values are on positive side of origin
  • – y-values are on negative side of origin
  • + slope indicates positive velocity
  • – slope indicates negative velocity
  • 0 slope indicates object is stationary
  • Changing slope indicates object is accelerating

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Velocity vs Time Graphs

What do we see in this graph?

  • Axes: v vs t
  • Changes in motion:
    • 0 s to 2 s: negative slope
    • 2 s to 6 s: zero slope
    • 6 s to 10 s: positive slope
    • 10 s to 14 s: negative slope
  • Crosses x-axis at 1 s and 8 s

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Velocity vs Time Graphs

 

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Velocity vs Time Graphs

What is the acceleration of the object at t = 4 s?

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What is the velocity of the object at t = 8 s?

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What is the acceleration of the object at t = 8 s?

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What would a qualitative “x vs t” graph for this “v vs t” graph look like?

We’ll look at how to determine displacement later.

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Velocity vs Time Graphs

  • + y-values indicate +v
  • – y-values indicate – v
  • + slope indicates positive acceleration
  • – slope indicates negative acceleration
  • 0 slope indicates constant velocity (no acceleration)
  • Crossing x-axis indicates change in direction
  • Changing slope (curve) indicates changing acceleration
  • Area under the curve represents displacement

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Displacement (Δx) From a �“v vs t” graph

The displacement of an object during a time interval is equal to the area under the curve of a graph of the object’s velocity as a function of time (i.e., the area bounded by the function and the horizontal axis for the appropriate interval).

Δx is total area

under the

curve.

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Change in Velocity (Δx) From an “a vs t” graph

The change in velocity of an object during a time interval is equal to the area under the curve of a graph of the acceleration of the object as a function of time.