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the physical quantity is distance and unit is meters
The slope of the speed/time graph is the magnitude of acceleration. (It's very difficult to draw a graph of velocity, unless the direction is constant.)
change in velocity
The radial velocity ie velocity towards or away from your starting point. It is NOT the ordinary speed or velocity because you can run in a circle around your starting point at top speed but the distance will not change so the slope of the distance time graph will be zero.
The slope of a line on a position vs. time graph would represent the a velocity of the object being described.