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### Variation Per Unit of Time

```
Date: 02/22/2002 at 05:38:45
From: John
Subject: Slope of a line and the variation per unit of time

Hi Dr. Math,

Suppose I have a graph that relates the position of a particle with
the time.

I can't understand why the slope of a line in a point corresponds to
the space that the particle runs per unit of time: why "per unit of
time"?
```

```
Date: 02/22/2002 at 09:23:09
From: Doctor Rick
Subject: Re: Slope of a line and the variation per unit of time

Hi, John.

In such a graph, the horizontal axis (most likely) represents time; it
should be marked in time units. The vertical axis represents the
position of the particle along a line. Thus the slope, which is the
change in vertical coordinate per unit of the horizontal coordinate,
is a rate of change of position per unit of time. For example, this
graph represents a particle moving 2 meters per second:

|            /
4 m +-----------/
|          /|
3 m +         / |
|        /  |
2 m +-------/   |
|      /|   |
1 m +     / |   |
|    /  |   |
----+---+---+---+--
1   2   3 sec

At time 2 seconds, the particle is 2 meters from the starting point on
the line. At time 3 seconds, the particle is 4 meters from the
starting point. Thus it moved 2 meters in 1 second.

Does it make sense yet?

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 03/05/2002 at 07:27:46
From: John
Subject: Slope of a line and the variation per unit of time

Thanks a lot for the explanation, it's great!
```
Associated Topics:
High School Equations, Graphs, Translations

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