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!