The shapes of the position versus time graphs for these two basic types of motion - constant velocity motion and accelerated motion i. The principle is that the slope of the line on a position-time graph reveals useful information about the velocity of the object. It is often said, "As the slope goes, so goes the velocity. If the velocity is constant, then the slope is constant i. If the velocity is changing, then the slope is changing i. If the velocity is positive, then the slope is positive i.
This very principle can be extended to any motion conceivable. Consider the graphs below as example applications of this principle concerning the slope of the line on a position versus time graph. The graph on the left is representative of an object that is moving with a positive velocity as denoted by the positive slope , a constant velocity as denoted by the constant slope and a small velocity as denoted by the small slope.
The graph on the right has similar features - there is a constant, positive velocity as denoted by the constant, positive slope. However, the slope of the graph on the right is larger than that on the left.
This larger slope is indicative of a larger velocity. The object represented by the graph on the right is traveling faster than the object represented by the graph on the left. The principle of slope can be used to extract relevant motion characteristics from a position vs. As the slope goes, so goes the velocity.
Consider the graphs below as another application of this principle of slope. The graph on the left is representative of an object that is moving with a negative velocity as denoted by the negative slope , a constant velocity as denoted by the constant slope and a small velocity as denoted by the small slope.
The graph on the right has similar features - there is a constant, negative velocity as denoted by the constant, negative slope. Once more, this larger slope is indicative of a larger velocity. As a final application of this principle of slope, consider the two graphs below. Both graphs show plotted points forming a curved line.
Curved lines have changing slope; they may start with a very small slope and begin curving sharply either upwards or downwards towards a large slope. In either case, the curved line of changing slope is a sign of accelerated motion i. Applying the principle of slope to the graph on the left, one would conclude that the object depicted by the graph is moving with a negative velocity since the slope is negative.
Furthermore, the object is starting with a small velocity the slope starts out with a small slope and finishes with a large velocity the slope becomes large. That would mean that this object is moving in the negative direction and speeding up the small velocity turns into a larger velocity. This is an example of negative acceleration - moving in the negative direction and speeding up. The graph on the right also depicts an object with negative velocity since there is a negative slope.
And one knows that an object is moving in the negative direction if the line is located in the negative region of the graph whether it is sloping up or sloping down. And finally, if a line crosses over the x-axis from the positive region to the negative region of the graph or vice versa , then the object has changed directions. Now how can one tell if the object is speeding up or slowing down? Speeding up means that the magnitude or numerical value of the velocity is getting large.
In each case, the magnitude of the velocity the number itself, not the sign or direction is increasing; the speed is getting bigger. Given this fact, one would believe that an object is speeding up if the line on a velocity-time graph is changing from near the 0-velocity point to a location further away from the 0-velocity point. That is, if the line is getting further away from the x-axis the 0-velocity point , then the object is speeding up.
And conversely, if the line is approaching the x-axis, then the object is slowing down. Consider the graph at the right. The object whose motion is represented by this graph is See Answer Answers: a, d and h apply.
FALSE since a negative velocity would be a line in the negative region i. Physics Tutorial. My Cart Subscription Selection. Student Extras. Time Graphs. FALSE since there is an acceleration i. TRUE since the line is approaching the 0-velocity level the x-axis.
FALSE since the line never crosses the axis. FALSE since the line is not moving away from x-axis. FALSE since the line has a negative or downward slope.
TRUE since the line is straight i. We Would Like to Suggest Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives.
We would like to suggest that you combine the reading of this page with the use of our Graph That Motion or our Graphs and Ramps Interactives. Each is found in the Physics Interactives section of our website and allows a learner to apply concepts of kinematic graphs both position-time and velocity-time to describe the motion of objects.
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