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1. The problem statement, all variables and given/known data

I was working on a kinematics experiment using Tracker to do a video analysis. I obtained a graph of displacement against time for the body under constant acceleration and the software also gives me the rms error between the parabolic trend line and the data points representing the position of the object over time.

However, I actually want the velocity-time function of the object but I do not want to rely on the software's algorithms to determine it. As such, I plan to find the derivative of the displacement-time trend line by hand however, is there a way to calculate the uncertainty in the derivative using the rms value of the original function?

2. Relevant equations

s(t) = At^2 + Bt + c

v = s'(t) = 2At + B

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# What is the uncertainty in the derivative of a function?

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