Thread: How would you do error analysis when using derivatives of a distance vs time graph?

***Supposing that the error for the distance is 0.05cm and the error for the time is 0.001 seconds and that I use the second derivitive of the fonction that represents my values to determine the acceleration.***

It is a very simple process (though not obvious):
Lets call ? the measurement error (so ?_x and ?_t are the measurement errors of position and time repectively)
We simply have to use partial derivatives of our equation for acceleration (a = d^2x/dt^2)

(?_a)^2 = ((?_x)*?a/?x)^2 + ((?_t)*?a/?t)^2

Where ?a/?x is the partial derivative of a with respect to x and ?a/?t is the partial derivative of a with respect to t.

Obviously the answer depends on your equation for x, so I can't solve this any further for you....
Just to clear up a few common misconceptions - you WILL have to plug in your values to the equation for X in order to get an error - which means the larger the value x you're measuring, the larger the error could be (also the shorter times you're measuring cause larger error).
But if you follow this approach you should be fine