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the difference between a constant in a graph and a constant in a experiment is that when on a graph, the constant is the thing that changes, and in a experiment it is the part that stays the same.
If constant motion means constant velocity then, total distance / total time = avg velocity => avg speed constant velocity => avg velocity = velocity
The graph of y = c, a constant will be a straight line parallel to the x-axis and c units from it..
You can't determine velocity from that graph, because the graph tells you nothing about the direction of the motion. But you can determine the speed. The speed at any moment is the slope of a line that's tangent to the graph at that moment.
linear?