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The key elements of a situation are visually represented in qualitative graphs. When a situation is described verbally, a rough sketch of its graph can be drawn. Consider the example.
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Example Situation |
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Paulina begins to run at a steady rate. While jogging downhill, she speeds up at an increasing rate. Her speed remains constant for a while. Finally, she begins to slow down at a steady rate until she comes eventually to a complete stop at the end of her run. |
The qualitative graph of such a situation can be drawn in two steps.
The graph can be temporarily split into four parts. These parts do not have to be placed at equal intervals because this is a rough sketch.
The starting point of the graph is the origin because the time Paulina starts running is considered to be 0 and her starting speed is 0. A constant rate means that the changes in one variable relative to another variable are always the same. This part of Paulina's run can be represented by a line segment with a positive slope starting from the origin.
Her speed then increases faster and faster as she runs downhill. This part of the graph can be drawn as a curve that becomes steeper.
After that phase, she runs at a constant speed — that is, her speed remains the same for an amount of time. This can be represented by a horizontal line segment.
Finally, her speed decreases at a constant rate for the rest of the run. This part should be a decreasing line segment and continue until it touches the horizontal axis.
As a final step, get rid of the temporary auxiliary lines.
This qualitative graph represents Paulina's speed throughout her run as described. Keep in mind that this is just a rough sketch. Due to a lack of numerical data, certain parts can appear longer, steeper, or flatter.