A graphical representation of the position of a moving object versus time gives you information about its speed, acceleration and direction of motion, and these can provide a wealth of other information. For example, plotting a graph of the distance of your car from home versus time can reveal information about the route you took, traffic conditions, engine performance and even your ability as a driver. A graph is a collection of points, and the points represent data that you collect by making measurements. The more measurements you make, the more accurate your graph will be.
Compile your data in a table that relates each measurement of position to the time at which it was taken. Decide on the most convenient units for each parameter. For example, if you're measuring movement of a ball in a laboratory, the best distance unit might be feet, while a workable time measurement may be seconds. If you're tracking the flight of a transcontinental airliner, you'll probably prefer kilometers or miles and minutes or hours.
Draw a pair of perpendicular axes on a sheet of graph paper with a sharp pencil. Label the vertical axis "distance" and the horizontal axis "time" and divide each axis into units in such a way as to be able to fit all your data on the graph. Distance increments of an inch and time increments of half a second might be appropriate for a ball in a laboratory. For an airliner, the increments might be 100 miles and 30 minutes for distance and time, respectively.
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Plot each point in your table on the graph by locating the distance measurement on the vertical axis and the time measurement on the horizontal axis. Draw a pair of perpendicular lines from each point, using a ruler, and make a cross with your pencil at their intersection point. You don't have to draw physical lines -- they can be invisible.
Look at the points to discern a pattern before drawing a line through them. They might all be close to a straight line or some other shape. Draw the line or curve that best approximates the shape they represent. Unless you noticed some irregular motion while making the measurements, about half of the points should be on one side of the curve and half on the other.
Compare the shape of the graph with the motion you observed to verify that it makes sense. The graph of the motion of a ball being thrown, for example, should display a decreasing slope as the ball gradually slows and falls. The slope on the graph of an airplane, on the other hand, should remain relatively constant throughout its flight.
The slope of the graph at any point on it denotes the speed of the object being monitored at that point in time. If the graph is curved at any point, it means the object is either accelerating or decelerating.
The slope of the graph can be 0 -- horizontal -- which means the object is at rest, but it can never be vertical. That would mean the object is moving with infinite velocity.
The starting point can be at (0,0), but it doesn't have to be. It can be anywhere on the vertical axis, meaning that the object began moving at some distance away from another reference point.