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

Oct 31, 2015

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 $a x + b$ $\to$ CONSTANT $k$;
QUADRATIC $a {x}^{2} + b x + c$ $\to$ LINEAR $a x + b$