Calculate Slope on Curves

MIT Demo Video

What’s the Point?

Using a spreadsheet to get an equation for a data that plots as a curve, it’s possible to get a very good estimate of the data values at all points, not just the ones you have data for. That equation can then be used for more calculations about the data.

TL;DW

  • Fitting a curve to a set of data can be used to get an approximate formula for the data. That allows calculating the X and Y values at any point, not just the ones the data has. In this case, the Y axis is the distance a ball has fallen and the X axis is how long it’s been falling.
  • By calculating the values of the formula for two points very close together, the slope can be quite accurately computed for any point on the curve. It doesn’t matter how far apart the points are, the slope is always the change in Y divided by the change in X.
  • For this curve with distance as the Y value and time as the X value, the slope between two points is the change in distance fallen between the points divided by the change in the time between them. Distance divided by time is velocity.

    \frac{\mathbf{.3\ meters}}{\mathbf{.15\ seconds}}\ =\ \mathbf{2}\ \mathbf{meters}\ \mathbf{per}\ \mathbf{second}

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