Estimate the Velocity Curve


In this step, you will plot the points representing an estimate of the car's speed versus time (you determined these points in the last step). Then you will find a curve that best fits those points. Then you will read off of this graph the time when the car's speed is zero -- this is the time it takes the car to come to a complete stop.

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 speed versus time: at time t = 0 the car's given speed is 88, at time t = 1 the car's speed was calculated to be 68. So, two of the points are (0, 88) and (1, 68).

In the "Fit Curve to Data" window, enter all the points into the table then press the "Your Data" button to plot the points. Here is what the first two points look like in the table:

Fill in the rest of the table with the rest of points you calculated. Note that you only need to use as many points as you need to get a good idea of what the graph looks like. Press the "Your Data" button to plot the points.

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.

Now you can estimate the time it takes the car to stop. The best fitting curve you have found is an estimate of the graph of the car's speed versus time. By looking at the graph, estimate the time it takes the car to stop. This is the time when the car's speed is 0 which is the same thing as the x-coordinate of the point where your curve intersects the x-axis (the x-axis is the time axis). You now have found an estimate of the time it takes the car to come to a complete stop.

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 speed as a function of time. You will use this equation in the next step.

Next: Follow the "Velocity Area" link to the left.


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