I am trying to write some functions to calculate the velocity, acceleration, and jerk (change in acceleration) of some valve motion data.

The data is typically about 220 points
The x axis is evenly spaced with an increment of 1
The y axis is provided in a list of "position data"


I would like to know the best way to accuratly calculate the
velocity, acceleration, and jerk of the y axis at each increment
along the x axis.


Below are two methods I have tried to calculate velocity at EXACTLY the point along the X axis of the distance measurment, obviouslyat least one of them is wrong.

Note: Calculating the velocity between two points is easy, the problem is finding the velocity on the point.


X Increment,    Y Position,    Velocity,    Avg Velocity,

1 -------------    1
           >-----------    1
2 -------------    2           >-----------    4.5 (velocity at 2)
           >-----------    8
3 -------------    10




X Increment,    Y Position,    Avg Position,    Velocity,

1 -------------    1
           >-----------    1.5
2 -------------    2             >----------    3.75 (velocity at 2)
           >-----------    6
3 -------------    10


Is there a better way to do this?/filter

The link below has the formulas.

Valve velocity ==> Three point rule for f'(x)

Valve acceleration ==> Three point rule for f''(x)

for jerk apply the f''(x) above to the velocity values instead of the position values.

h= increment

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