

Lesson 1: Describing Motion with WordsIntroduction to the Language of Kinematics 
Lesson 3 : Describing Motion with Position vs. Time GraphsThe Meaning of Slope for a pt GraphAs discussed in the previous
part of Lesson 3, the slope of a position vs. time graph
reveals pertinent information about an object's velocity.
For example, a small slope means a small velocity; a
negative slope means a negative velocity; a constant slope
(straight line) means a constant velocity; a changing slope
(curved line) means a changing velocity. Thus the shape of
the line on the graph (straight, curving, steeply sloped,
mildly sloped, etc.) is descriptive of the object's motion.
In this part of the lesson, we will examine how the actual
slope value of any straight line on a graph is the velocity
of the object. Consider a car moving with a constant velocity of +10 m/s for 5 seconds. The diagram below depicts such a motion.
The positiontime graph would look like the graph at the right. Note that during the first 5 seconds, the line on the graph slopes up 10 m for every 1 second along the horizontal (time) axis. That is, the slope of the line is +10 meter/1 second. In this case, the slope of the line (10 m/s) is obviously equal to the velocity of the car. We will examine a few other graphs to see if this a principle which is true of all position vs. time graphs.
Now consider a car moving at a constant velocity of +5 m/s for 5 seconds, abruptly stopping, and then remaining at rest (v = 0 m/s) for 5 seconds.
If the positiontime data for such a car were graphed, then the resulting graph would look like the graph at the right. For the first five seconds the line on the graph slopes up 5 meters for every 1 second along the horizontal (time) axis. That is, the line on the position vs. time graph has a slope of +5 meters/1 second for the first five seconds. Thus, the slope of the line on the graph equals the velocity of the car. During the last 5 seconds (5 to 10 seconds), the line slopes up 0 meters. That is, the slope of the line is 0 m/s  the same as the velocity during this time interval.
Both of these examples reveal an important principle. The principle is that the slope of the line on a positiontime graph is equal to the velocity of the object. If the object is moving with a velocity of +4 m/s, then the slope of the line will be +4 m/s. If the object is moving with a velocity of 8 m/s, then the slope of the line will be 8 m/s. If the object has a velocity of 0 m/s, then the slope of the line will be 0 m/s.

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