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Understanding Graphs of Motion: Giving Qualitative Descriptions

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  • 0:01 No Math Today
  • 0:26 Qualitative Graphing
  • 1:45 Basic Graph Shapes
  • 4:52 Lesson Summary
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Lesson Transcript
Instructor: Angela Hartsock

Angela has taught college Microbiology and has a doctoral degree in Microbiology.

You can just look at graphs of straight line motion and accurately describe how that object is moving. In this lesson, we will investigate the basic shapes the graphs can take and what conclusions you can draw from these shapes.

No Math Today

For some of you out there, I have some good news. This kinematics lesson will not include any numbers or math. At this point, you should know how to perform all the necessary calculations with Position vs. Time and Velocity vs. Time graphs. Now, we're going to see what we can figure out just by looking at the shapes of these graphs, no numbers required.

Qualitative Graphing

If I show you two different Position vs. Time graphs and ask you to tell me which one represents an object traveling at a constant velocity, you should have no problem figuring it out.

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After all, this graph shows the position and the time both changing at a constant rate. The second graph shows an object that is not moving. If you had to, you could calculate the slopes of the graphs and give me the velocity. But, what if I take away all the numbers? Can you still pick out the graph of constant velocity? Of course you can. The graph still shows the position and time changing at a consistent rate even though I've taken away the actual values.

What you've just done is make a qualitative assessment of the graph and used it to describe the motion of the object. With qualitative graphing you are describing the motion of an object by recognizing the basic shapes on its graph, not through exact calculations.

The best way to proceed is to look at the seven basic shapes of Velocity vs. Time and Position vs. Time graphs. By the end, you should be able to quickly recognize what's going on in each graph, what a specific type of motion looks like on both types of graphs, and how to sketch one type of graph if given the other type. Let's dive right in.

Basic Graph Shapes

Here's #1.

1: The object is not moving.

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As you can see, the position is not changing on the first graph, and the velocity is 0 m/s on the second. Here, you are simply standing still.

2: The object is moving at a constant velocity in the positive direction.

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Here, position and time are changing at a constant rate, upwards. The velocity graph is horizontal, above the time axis. Now, you are walking a steady pace forward.

3: The object is moving at a constant velocity in the negative direction.

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These graphs are the opposite of #2. Position is constantly changing downward. Velocity is a horizontal line below the time axis. Back at the starting point, you decide to walk backwards at a steady pace.

4: The object is speeding up (or accelerating) in the positive direction.

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The Position vs. Time graph shows an object that is moving faster as time passes, drawn as a curve. The velocity graph is increasing constantly, in a straight line. A steady speed won't cut it anymore. You start walking slowly but steadily move faster until you're running forward.

5: The object is slowing down in the positive direction.

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These graphs show the opposite of #4. The change in position decreases as time passes. The velocity steadily decreases. This time, you are already running forward at the start but gradually slow down to a stop.

6: The object is slowing down in the negative direction.

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