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The best-fit line represents our best estimete of what the graph would look like if the cars did travel at a constant speed, and if our measurements were perfect. Looking at one best-fit line, you will see that some of the data points are above it and some below, but it is the straight line that is as close as possible to all the data points. They don't go exactly through all the data points themselves instead, they are called best-fit lines, and represent the trend of the numbers. Notice the black lines that run through the cars' data points on the graph. The data points do not form a perfectly straight line, because (1) perhaps the car did not maintain a perfectly constant speed, or (2) even if the car had a constant speed, the measurements may have slight errors. The small car was the faster of the two, and this is reflected in the steepness of the line. Both cars traveled 9 meters, but the small car did it in less time (about 17 sec) than the big car (about 36 sec). The vertical axis is the position of the car, x, measured in meters. (Click it if you'd like a larger version.) Here is the resulting graph of position, x, as a function of time, t. This process was then repeated with another, smaller toy car. When released from the starting line, the stopwatch was started, and the time that it crossed each subsequent meter was recorded. Let's start with graphing the position first.Īs an example, we took a toy motorized car, and set it rolling along a nine-meter-long track, our x-axis. Understanding motion is greatly helped by graphing the position of the object as a function of time, and also the object's velocity as a function of time.