This is an example of positive acceleration. So this object is moving in the negative direction and slowing down. The object begins with a high velocity (the slope is initially large) and finishes with a small velocity (since the slope becomes smaller). The graph on the right also depicts an object with negative velocity (since there is a negative slope). This is an example of negative acceleration - moving in the negative direction and speeding up. That would mean that this object is moving in the negative direction and speeding up (the small velocity turns into a larger velocity). 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). 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 ). In either case, the curved line of changing slope is a sign of accelerated motion (i.e., changing velocity). 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. Both graphs show plotted points forming a curved line. Slow, Leftward(-)Īs a final application of this principle of slope, consider the two graphs below. The object represented by the graph on the right is traveling faster than the object represented by the graph on the left. Once more, this larger slope is indicative of a larger velocity. However, the slope of the graph on the right is larger than that on the left. The graph on the right has similar features - there is a constant, negative velocity (as denoted by the constant, negative 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). Slow, Rightward(+)Ĭonsider the graphs below as another application of this principle of slope. The principle of slope can be used to extract relevant motion characteristics from a position vs. This larger slope is indicative of a larger velocity. The graph on the right has similar features - there is a constant, positive velocity (as denoted by the constant, positive slope).
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). This very principle can be extended to any motion conceivable.Ĭonsider the graphs below as example applications of this principle concerning the slope of the line on a position versus time graph.
If the velocity is positive, then the slope is positive (i.e., moving upwards and to the right). If the velocity is changing, then the slope is changing (i.e., a curved line). If the velocity is constant, then the slope is constant (i.e., a straight line). It is often said, "As the slope goes, so goes the velocity." Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa). The principle is that the slope of the line on a position-time graph reveals useful information about the velocity of the object. The shapes of the position versus time graphs for these two basic types of motion - constant velocity motion and accelerated motion (i.e., changing velocity) - reveal an important principle.
time graphs for the two types of motion - constant velocity and changing velocity ( acceleration) - are depicted as follows. Note that a motion described as a changing, positive velocity results in a line of changing and positive slope when plotted as a position-time graph. If the position-time data for such a car were graphed, then the resulting graph would look like the graph at the right.
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