A distance-time graph shows the movement of an object with respect to time.
The average slope between any two points on the graph is equal to the average velocity of the object between those two points.
The instantaneous slope (or derivative) at a point on the graph is equal to the instantaneous velocity of the object at that point.
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A distance time graph would show the distance traveled.
There are many things the graph does not show. It does not show my shoe size, for example.
The distance from start at which a certain object is located at a certain time.
acceleration.
a vertical one