XVA - Constant Position

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Here we are looking at the simplest type of motion, that of an object which is standing still. Perhaps many would not even consider this a type of motion, but it is a starting point from which to understand more and more complicated motions.

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[1] Here is the first of our constant position examples. The object is resting at the origin of its position number line, and time is passing. It is standing still at x = 0.0 m.

Parameters:

xo = 0.0 m vo = 0.0 m/s a = 0.0 m/s2 The object's position starts at 0.0 m, and it stays at that location as time passes. The object's velocity starts at 0.0 m/s. It's velocity remains at that value as time passes. The constant acceleration is 0.0 m/s2; so, the velocity does not change as time passes.

[1] Java applet demonstration

Comments:

• The object is standing still.
• In all three of the above graphs the graph line of the function is drawn directly over the time axis. Therefore, it may at first be difficult to realize that there is actually data expressed on these graphs.

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[2] The object here is also standing still. Unlike the object in [1] above, however, this object is not located at the origin. It starts out 40.0 meters away from the origin in the positive direction. It stays there.

Parameters:

xo = 40.0 m vo = 0.0 m/s a = 0.0 m/s2 The object's position starts at 40.0 m, and it stays at that location as time passes. The object's velocity starts at 0.0 m/s. It's velocity remains at that value as time passes. The constant acceleration is 0.0 m/s2; so, the velocity does not change as time passes.

[2] Java applet demonstration

Comments:

• The object is standing still at a place 40.0 m from the origin.

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[3] These opening examples are simple. They are included here to make sure that a fundamental understanding of these three graphs is present from the easiest beginnings. Here the object is motionless, located positive 80.0 meters from the origin.

Parameters:

xo = 80.0 m vo = 0.0 m/s a = 0.0 m/s2 The object's position starts at 80.0 m, and it stays at that location as time passes. The object's velocity starts at 0.0 m/s. It's velocity remains at that value as time passes. The constant acceleration is 0.0 m/s2; so, the velocity does not change as time passes.

[3] Java applet demonstration

Comments:

• Again, the object standing still at another place. This is much like the object that is standing still in example [2].

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[4] Be sure you understand what we mean by negative positions. Here, the object is remaining motionless and located at x = -40.0 meters. That is, it is on the other side of the origin than the side it was on in the above three examples.

Parameters:

xo = -40.0 m vo = 0.0 m/s a = 0.0 m/s2 The object's position starts at -40.0 m, and it stays at that location as time passes. The object's velocity starts at 0.0 m/s. It's velocity remains at that value as time passes. The constant acceleration is 0.0 m/s2; so, the velocity does not change as time passes.

[4] Java applet demonstration

Comments:

• Note that the object's original position can be at a negative or positive coordinate.
• Usually, problems are set up so as to consider the object starting at the origin. But that is not always the case, nor is it always desirable to set up a problem that way. So, one must understand what is meant by having the object start at a positive or negative position.

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[5] This is another example of an object standing still at a negative position. Here, the object is remaining motionless and located at -80.0 meters.

Parameters:

xo = -80.0 m vo = 0.0 m/s a = 0.0 m/s2 The object's position starts at -80.0 m, and it stays at that location as time ticks on. The object's velocity starts at 0.0 m/s. It's velocity remains at that value as time ticks on. The constant acceleration is 0.0 m/s2; so, the velocity does not change as time ticks on.

[5] Java applet demonstration

Comments:

• Another object standing still at another negative coordinate position. This is much like the object that is standing still in example [4].

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