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A suitable approach to this question involves analyzing the velocity-time graph in order to develop a verbal description of the moving object it represents. Then match the verbal description to the particular features of a position-time graph would be consistent with such a motion.
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The velocity-time graph displays a horizontal line located in the positive region of the graph (above the time axis). The horizontal line represents a motion with a constant velocity. Since only positive velocity values are plotted, the object has a positive velocity the entire time. Thus, the graph represents an object moving with a constant positive velocity.
A constant velocity motion is represented on a position-time graph by a straight diagonal line. A positive velocity is represented on a position-time graph by a line with positive slope.
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Velocity-Time Graphs:
Velocity versus time graphs represent changes that occur in an object's velocity with respect to time. These graphs most commonly display horizontal lines or straight diagonal lines. Horizontal lines represent an object with a constant velocity. If the horizontal line is on the time axis, the object is at rest (a constant velocity of 0 m/s). If the horizontal line is above or below the time axis, then the object is moving with a constant positive or a constant negative velocity. Straight diagonal lines represent an accelerated motion. The slope of the line is the acceleration of the object.
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Position-Time Graphs:
Position versus time graphs represent changes that occur in an object's position with respect to time. These graphs most commonly display horizontal lines, straight diagonal lines and curved lines. Horizontal lines represent an object at rest. Straight diagonal lines represent a constant speed motion. Curved lines represent an accelerated motion. The slope of the line is the velocity of the object. Steeply-sloped lines represent fast-moving objects. Gently-sloped lines represent slow-moving objects.
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