Variation Per Unit of TimeDate: 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! |
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