infinite speed
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Object will change distance time graph when speed is changing. Distance time graph don't changed indicate of the stationary.
The line would indicate motion at a constant speed.
No: not until instantaneous teleportation is discovered.
On a typical graph, the vertical line is the y-axis, they horizontal line is the x-axis.
Test it by the vertical line test. That is, if a vertical line passes through the two points of the graph, this graph is not the graph of a function.