{"id":14253,"date":"2022-01-24T12:21:32","date_gmt":"2022-01-24T20:21:32","guid":{"rendered":"https:\/\/www.vernier.com\/til\/?p=14253"},"modified":"2025-05-12T08:08:14","modified_gmt":"2025-05-12T15:08:14","slug":"what-are-my-velocity-calculations-options-in-vernier-video-analysis","status":"publish","type":"post","link":"https:\/\/www.vernier.com\/til\/14253","title":{"rendered":"Are there different ways to calculate velocity in Vernier Video Analysis?"},"content":{"rendered":"

In Vernier Video Analysis, velocity is calculated using a numerical derivative. The default calculation uses seven points, three on either side of the position point of interest, to calculate the object’s velocity at the point of interest (for additional details, see https:\/\/www.vernier.com\/til\/1011<\/a><\/a>). While useful for reducing the effect of point-marking inconsistencies, the calculation is problematic when changes in position happen rapidly, such as when an object collides with another object. Often in such situations, the goal is to determine the velocity of the object just before or just after the collision. However, the numerical derivative calculation provides a poor estimate for the velocity in which you are interested. <\/p>\n

Figure 1 shows typical data for a bouncing ball. As expected for an object in freefall, the velocity appears linear while the ball is in the air. The velocity values do not follow this pattern at the bounce point because the velocity calculations use position data from both sides of the bounce. The number of velocity points affected (i.e., they don\u2019t follow the linear pattern) is directly related to the number of points used in the numerical derivative calculation.<\/p>\n

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Figure 1 \u2013  Position and velocity <\/em>vs. time graphs for a bouncing ball<\/em> <\/figcaption><\/figure>\n<\/div>\n

What follows are three options for obtaining a more accurate estimate of velocity for situations in which position changes rapidly, such as a  bouncing ball. Not every method will work in every situation, so you will want to select the method that works best for your data. <\/p>\n

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1. Adjust the Number of Points in the Velocity Calculation<\/h3>\n

A custom calculated column can be used to calculate velocity using fewer than the default seven points. Follow these steps to create the calculated column:<\/p>\n

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  1. Click or tap Columns Options, \"\", for any column in the data table, and select Add a Calculated Column.\u00a0<\/li>\n
  2. Enter a Name and Units for your column.\u00a0<\/li>\n
  3. Click or tap Insert Expression and select Custom Expression.\u00a0<\/li>\n
  4. Enter the expression firstDerivative(Y, X, n)<\/strong> where Y is the position column, X is the time column, and n is the number of points used in the derivative calculation. Follow these guidelines when entering the expression:\n