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A suitable approach to this question involves analyzing the position-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 velocity-time graph would be consistent with such a motion.
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The position-time graph displays a curved line with positive slope. The positive slope represents an object with a positive velocity. The curve represents an object that is accelerating. The curve starts with a gentle slope and begins to get steeper and steeper. Since the velocity of the object is represented by the slope of the line, the increase in slope means the object is speeding up. Thus, the graph represents an object moving in the positive direction, speeding up the entire time.
An accelerated motion on a velocity-time graph is represented by a diagonal line. A positive velocity on a velocity-time graph is represented by a line located in the positive region of the graph (above the time axis). An object that is speeding up is represented on a velocity-time graph by a line that starts near the time axis (close to 0 m/s) and begins to move away from the time axis.
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Velocity-Time Graphs:
Velocity versus time graphs represent changes which 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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