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Motion in a position-time graph is relative to the starting position and depicted by the direction of the line on the graph, or slope. A positive slope describes movement or velocity in a positive direction, while a negative slope describes movement or velocity in a negative direction.
The slope of a position graph represents the velocity of the object. So the value of the slope at a particular time represents the velocity of the object at that instant.
If the velocity is constant, then the slope is constant (i.e., a straight line). If the velocity is changing, then the slope is changing (i.e., a curved line). If the velocity is positive, then the slope is positive (i.e., moving upwards and to the right). This very principle can be extended to any motion conceivable.
If we make a graph of position vs time and our object is moving at a constant velocity, the graph will form a straight line.
The key to using position-time graphs is knowing that the slope of a position-time graph reveals information about the object's velocity. By detecting the slope, one can infer about an object's velocity. "As the slope goes, so goes the velocity."