Linear graph. Distance versus time. Speed versus time

Distance versus time graphs. Speed versus time graphs.

Distance versus time graphs and speed versus time graphs are linear graphs. In linear graphs we can analyzed how varies one magnitude with respect another variable. Let see the steps to construct a good linear graph.   

1. Have data ready to plot as points on a graph. If you haven't already done so, create a table/chart in which one column is the time and one column is the distance. Fill in the time paired with the distance traveled (the data may be presented to you in paragraph form, in a list or in a table included in the question).

2. Draw two perpendicular lines that intersect on the graph paper, leaving a margin of three or four boxes between the axes and the edges of the paper. Draw arrows at the ends of the lines. Note that the x axis is the horizontal line and the y axis is the vertical line.

Axis [ak-sis], (plural ax·es [ak-seez]) -- one of two (or three) reference lines used in the coordinate system to locate a point (x,y) in a plane (or in space using a third axes, z, plotting (x,y,z) points).

3. Label the axes. x is normally independent but y depends on x. Time will be graphed on the x-axis, because time does not depend on distance (distance is dependent), because the "distance covered does depend on the time" -- how long you spend traveling at a certain rate -- which will be measured on the y-axis. Label the x-axis "Time" (t), and write the units (usually seconds, or s) in parentheses under "Time". Make the y-axis, using "Distance" (d) and the unit of distance often meters, m, or kilometers (km) or miles, etc.).

4. Begin plotting (graphing points) based on your (time, distance) data pairs (t,d) = (x,y); remember we are substituting t for x, and d for y. Continue using your data and graphing the points until you've finished with all your data; for example (2,5) means place a point/small dot using x = t = 2 and y = d = 5.

How? Look across the x-axis for +2, then go straight up +5 units, place your dot there. That is the (x,y) point for (t,d) = (2,5). Note: x is measured across and y is measured up and down.

5. After all the points have been plotted, take a straight edge (preferably a ruler) and connect the dots from the lowest X axis measurement to the highest measurement.

Remember a good graph contains the:

• o    Title,
• §  Include the data and object that is being studied -- e.g., "The Time/Distance Ratio of a Tennis Ball"
• o    Labeled axes,
• o    Numbered scale on each axis.

These steps will be the same any time that we want to draw a linear graph. The changes will be relating with the magnitudes we need to represent.

In linear graphs the axis are not only provided information also the slope (line that connects all the point in the graphic) is a good source of information. In distance versus time graph the slope indicates the speed of the object; and in a speed versus time graph the slope indicates the acceleration of the object.

For calculate slope we are going to use the following formula

slope=rise/run

rise is how much change the y axis from one point to the next point.

run is how much change the x axis from one point to the next point.

In a distance versus time graph slopes equal to zero means that the object does not move, because it is not changing its distance, the object is in rest.

In speed versus time graph slopes equal to means that the object moves at a constant speed, the speed does not change.