Estimate the Distance Curve


In this step, you will plot the points representing an estimate of the car's distance versus time (you determined these points in the last step, called "Velocity Area"). Then you will find a curve that best fits those points. That curve will give the car's distance as a function of time. You will use this distance function to calculate the car's distance at the time when the car's speed is zero -- this is the distance it takes the car to come to a complete stop. Note that this step is very similar to the step you previously took (called "Velocity Curve") to find the car's speed curve.

You will need to use the "Fit Curve" tool to accomplish this. Under "Tools" to the left, press the "Fit Curve" button. A separate window, named "Fit Curve to Data," should pop up in which you will plot the points.

This tool is easy to use -- click the demo button for a quick demonstration of how to use it. If you're still having trouble understanding it, then try the "Help" button.

From the previous step, you have a set of points representing an estimate of the car's distance versus time. You want to find a smooth curve that goes through (or comes as close as possible to going through) these points. Enter these points into the table in the "Fit Curve to Data" window. This is done similar to entering the car's speed and time into the same table when you found the car's speed as a function of time in the "Velocity Curve" step.

Once you have entered all the points into the table then press the "Your Data" button to plot the points. Note that you only need to use as many points as is necessary to get a good idea of what the graph looks like.

Now you want to find a smooth curve that will pass through, or come as close as possible to passing through, all the points. You will need to

  1. Choose a function type, and
  2. Adjust the parameters (A, B, C, D) until the curve fits the data.

So, for a chosen function type, you will repeatedly adjust the parameters then try them (by pressing the "Try The Above Coefficients!" button) until you find a curve that "best" (what does best mean?) fits your points. You will want to write down the equation of your best fitting curve by noting the parameters you have chosen. You will probably want to try more than one function type to see if you can find a curve that fits even better.

Write down the equation of the curve you have found that fits your data points the best. This equation is an estimate of the car's distance as a function of time.

Now, take the time it takes the car to come to a complete stop (you estimated this time in the "Velocity Curve" step when you found the time when the car's speed is 0), and plug it into the car's distance function you just found (if you need, use a calculator by pressing the "Calculator" button to the left). The distince you calculate is your estimate of the distance it takes the car to come to a complete stop.

Question: Did the car stop before it hit the other cars that were 88 feet further down the road when the car started it's skid?

Next: Follow the "Check Answer" link to the left.


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