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Position-Time Graphs:
Position versus time graphs represent changes that occur in an object's position with respect to time. The slope of the line is the velocity (change in position divided by the change in time) of the object.
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The oil drop pattern uses dots to represent the location of the car after a certain interval of time - perhaps after every 1-second interval in time. An inspection of the location of each dot relative to the previous dots allows you to determine if the distance traveled in the most recent second is increasing, decreasing or staying the same. You can decide what type of motion is involved by observing how the distance traveled in each consecutive second is changing.
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It should be clear from the oil drop pattern that the object is moving with a changing velocity. The object changes its speed from a large velocity (fast) to a small velocity (slow). The velocity is negative the entire time. You must match this with the appropriate position-time plot. As mentioned in the Know the Law section, the slope of a position-time graph is equal to the velocity. As the slope goes, so goes the velocity. Since the velocity is changing, the slope of the line should be changing. This restricts your options to one of the four curves. Since the velocity is negative, you will have to choose a curve that has negative slope. And finally, you will have to select the curve that starts with a large slope (for fast) and finishes with a small slope (for slow).
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