What is how does a motion graph of distance vs time differ from a graph of speed vs time?
Have a look if it makes sense.
The two graphs are connected because the speed vs time is a graph of the slopes obtained from the distance vs time graph:
1) consider a particle moving with constant speed:
The distance vs time graph is a linear function while the speed vs time is a constant;
2) consider a particle moving with varying speed (constant acceleration):
The distance vs time graph is a quadratic function while the speed vs time is a linear;
As you can see from these examples the speed vs time graph is the graph of a function of