How do you determine the uncertainty of a derived quantity?

To determine the uncertainty of a derived quantity, you must consider the uncertainties of the measured quantities used in the calculation.

When calculating a derived quantity, you are combining two or more measured quantities. Each of these measured quantities has its own uncertainty, which must be taken into account when determining the uncertainty of the derived quantity. The general rule is that the uncertainty of a derived quantity is equal to the square root of the sum of the squares of the individual uncertainties.

For example, if you are calculating the velocity of an object using the equation v = d/t, where d is distance and t is time, you must consider the uncertainties in both distance and time. If the distance has an uncertainty of ±0.1 m and the time has an uncertainty of ±0.05 s, then the uncertainty in the velocity is given by:

√(0.1² + 0.05²) = ±0.11 m/s

It is important to note that this method assumes that the uncertainties in the measured quantities are independent and random. If there are systematic errors or correlations between the measured quantities, then a more complex analysis may be required.

In summary, to determine the uncertainty of a derived quantity, you must consider the uncertainties of the measured quantities used in the calculation and use the square root of the sum of the squares of the individual uncertainties.