Question

What is how does a motion graph of distance vs time differ from a graph of speed vs time?

Answer 1

Have a look if it makes sense.

Explanation:

The two graphs are connected because the speed vs time is a graph of the slopes obtained from the distance vs time graph:

For example:

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 `1` degree less than the distance vs time function:
LINEAR `ax+b` `->` CONSTANT `k`;
QUADRATIC `ax^2+bx+c` `->` LINEAR `ax+b`