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

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

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Answer 1 · 2015-10-31T22:08:13

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:
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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):
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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 $1$ $1$ degree less than the distance vs time function:
LINEAR $a x + b$ $ax+b$ $\to$ $->$ CONSTANT $k$ $k$ ;
QUADRATIC $a x^{2} + b x + c$ $ax^2+bx+c$ $\to$ $->$ LINEAR $a x + b$ $ax+b$

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

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