Describing Motion with Position vs. Time Graphs
Explore the relationship between graphs and motion with The Moving Man simulation from PHET.Graph Matching Motion Model
This EJS simulation from Open Source Physics (OSP) contrasts the graphs for constant speed and accelerated motion.Shockwave Studios
Graph That Motion from the Shockwave Studios is an excellent accompanying activity to this page.The Laboratory
Looking for a lab that coordinates with this page? Try the Position-Time Graphs Lab at The Laboratory. Requires motion detectors.Curriculum Corner
Learning requires action. Give your students this sense-making activity from The Curriculum Corner.Treasures from TPF
Need ideas? Explore The Physics Front's treasure box of catalogued resources on kinematic graphing.
The Meaning of Slope for a p-t Graph
As 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 position-time 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 that 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 position-time 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 position-time 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.