Two students want to measure the acceleration a of a cart rolling down an inclined plane. The cart starts at rest and travels a distance s down the plane. The first student estimates the acceleration by measuring the instantaneous velocity v just as the cart has traveled s meters, and uses the formula 
The second student estimates the acceleration by measuring the time, in seconds, that the cart takes to travel s meters, and uses the formula 
. Assume that s=1 m, and that there is negligible uncertainty in s. Assume that v=3.2 ± 0.1 m/s and that t=0.63 ± 0.01 s. Assume that the measurements of v and t are independent.
a. Compute the acceleration using the method of the first student. Call this estimate 
. Find the uncertainty in .
b. Compute the acceleration using the method of the second student. Call this estimate 
. Find the uncertainty in .
c. Find the weighted average of 
and 
that has the smallest uncertainty. Find the uncertainty in this weighted average.
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