Video: Position-Time Graph ... Conceptual Analysis

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Position-Time Graphs: Conceptual Analysis
 Video Transcript

The Questions
How can a description of an object's motion be determined from a position-time graph? 
And how can a position-time graph be related to other representations of an object's motion ... like dot diagrams?
I'm Mr. H and I have some answers for you.

Position-time graphs (or p-t graphs) show an object's position as a function of time. The manner in which an object moves affects the look of the graph - like whether it is horizontal, straight and diagonal, or curved. Let's talk about the details.

Relating Graph Features to Motion
Suppose an object is stationary, keeping the same position for some time. The p-t graph will be a horizontal line. But if its moving, the line will have some sort of slope. It could be a straight, diagonal line or a curved line. But it won't be horizontal. 
The slope could be positive - "upward sloped" - which indicates that the object is moving in the positive direction. And if the slope is negative - "downward sloped" - the object is moving in the negative direction. In Physics, we usually designate rightward as the positive direction; that makes leftward the negative direction.
You've likely noticed that some p-t graphs have straight, diagonal lines and others have curved lines. What's up with that?  A straight, diagonal line indicates a constant velocity motion. This p-t graph shows an object moving right at a constant velocity and this one shows moving left at a constant velocity. 
If you ever have to make speed comparisons between objects, then focus on the steepness of the lines that represent their motion. Steeper lines are for faster objects; flatter or shallower lines represent slower objects. This idea of steepness applies to negative sloped lines as well.
Curved lines on p-t graphs indicate that the object is changing its velocity - like from slow to fast or from fast to slow. Here's four different curved lines. Two of them become steeper over the course of time. They represent an object that is getting faster or speeding up. You can tell this when you notice the line starts flat and finishes steep. The other two p-t graphs have lines that start steep and finish relatively flat. This indicates a getting slower or slowing down motion. Just like straight, diagonal lines, curved lines indicate the direction of motion by an upward or a downward slope.

Relating Graph Features and Dot Diagrams
Like p-t graphs, dot diagrams represent an object's position over the course of time. Each dot might represent the position at 1-second intervals of time. Arrows are used to indicate the direction the object moves. When the dots are close together, you would reason that the object is moving slow. When the dots are further apart, the object is moving fast. Evenly-spaced dots indicate constant speed motions. But if the dot spacing changes over the course of time, you know the object is speeding up or slowing down.
If you have to relate a dot diagram to a p-t graph, here's a great strategy. Analyze the dot diagram and describe the motion in words. Then relate the words to the features of a p-t graph. Here's an example. The dots indicate an object moving fast in the negative direction. So the graph that matches this will be steep (which means fast) and have a negative slope (which means moving in the negative direction).
Hey - You Got This!

In the Description section of this video, you will find links to some awesome interactive exercises on our website. The best way to ensure Physics understanding is to apply the concepts you're trying to understand. So give one of them a try. 
I'm Mr. H. Thanks for watching!  


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