Question

Suppose I measure the velocity of an object at two different times, t1 and t2. If I tell you that the uncertainty in velocity is 0.1 m/s for each point, then calculate the uncertainty in acceleration if t1 = 0.0 s and t2 = 0.01s.

Answer 1

a=1/deltaT (v2-V1) where V2=a+-deltaV2 and V1=b+-deltaV1

lets do some math:

a= 1/deltaT (a+-deltaV2-b+-deltaV1)

taking the partial deriviatives

deltaacc= 1/deltaT *(+-deltaV2+-deltaV1)

so the
uncertainity in acceleration is

1/.01 ( +-.2)=+-20m/s^2

Now, this all assumes the uncertainty in velocities are not independent. If you know the uncertainty is independent, and random, then using statistical standard deviations, uncertainty in acceleration is

deltaA=1/deltaT * sqrt 2(.1/)^2 or
deltaA= 100*.1*sqrt2= +-14

http://www.rit.edu/cos/uphysics/uncertainties/Uncertaintiespart2.html