Motion In One Dimension Worksheet (MOW) is a flexible tool for creating sheets of one dimensional data. Data in one dimension can be printed or displayed in other ways such as on a computer screen, poster, or just typed on the page. By using the MOW itself, data is automatically arranged in various dimensions such as on a flat surface, a two-dimensional surface, or even in three dimensions. This feature of the worksheet is very convenient for the data user and an advantage over other data management products. A quick example of how it works is as follows.
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Let us say that we have two sets of data, say x and y. Each set is then measured and recorded at different times. The third set is then compared to the first set to see which set of data best represents the movement of the object. To do this, we must know what coordinate system to use since there are five coordinate systems commonly used when working with motion.
These coordinate systems are based on numbers that refer to the longitude and latitude, east/west directions, south/west directions, east/west coordinates, and elevation. Longitude and latitude numbers are positive numbers while east/west numbers are negative numbers. In order to make our comparison easier, it is convention to always use the positive numbers.
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Now we know which coordinate system to use, all that remains is to calculate the data points on the different coordinate systems. For each point we plot a line connecting them so that their data value appears on the x axis and their point of origin on the y axis. Since each point represents a data point, it can be said that each point is a point on a plane. To transform the data into a plane, we add some constant values such as the slope or level of the surface or whatever the underlying surface is.
Here is a quick example showing the usage of x and y coordinate systems to calculate motion in one dimension. Assume you have a point P on your x-axis plane. You then take a snapshot of it by moving your mouse to P and clicking. The resulting data set would be (P, y) where P is along the x axis, and y is along the y axis.
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If P is moving east at a rate of 10 meters per second, it will be displayed as (P, 10). The slope of this surface is -10 meters per second. Using (P, y) as your point of origin and moving east, the horizontal coordinates would now be (x, y). This is a useful way to plot lines from point A to point B on the x or y axis. You can also plot horizontal lines from point A to point B along the x axis.
If P is moving west at a rate of 10 meters per second, it would be displayed as (P, 15). This is plotted using data that has been fitted to the point P. The slope of the data set is still (P, 15). The main point here is that the data plot has been fitted to the point P. There is now only one data point used to determine the motion of P along the x axis. If the data were plotted without any reference point, there would be numerous zigzags in the data points.
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Motion in one dimension is normally expressed as a mathematical function such as sin(x) where x is measured in degree (pi), where h is the horizontal coordinate, and t is the vertical coordinate. The equation to describe the motion on the x axis is: h(x) = sin(x) * sin(x)
In order for this to work, there must be some constant. This could be acceleration, the velocity at which the object is traveling, or time. The time constant t can be thought of as being equal to the period of time it takes for an impulse to move from a point A to B. The acceleration, however, must not be negative. Instead it should be positive, that is, it should go up as the object moves along the x axis and down as the object moves along the y axis. The time constant can be thought of as being equal to the rate of change of the acceleration along the x and y axes.
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