Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s due to human reaction time at the start a d stop moments. What is the percent uncertainty of a hand-timed measurement of (a) 5.5 s, (b) 55 s, (c) 5.5 min?

The uncertainty in measurement is defined as the variation of the values that are assigned to a particular quantity.

The formula of percent uncertainty is

\(\Delta T = \frac{{{T_1}}}{{{T_2}}} \times 100\% \) . … (i)

The uncertainty in measurements with a stopwatch\({T_1} = 0.{\rm{2 s}}\).

The given hand-timed measurement is\({T_2} = 5.{\rm{5 s}}\).

From equation (i), the percent uncertainty is:

\(\begin{aligned}{c}\Delta T = \frac{{0.2}}{{5.5}} \times 100\% \\ = 3.64\% \\ \approx 4\% \end{aligned}\).

Thus, the percent uncertainty is 4%.

The given hand-timed measurement is\({T_2} = 5{\rm{5 s}}\).

From equation (i), the percent uncertainty is

\(\begin{aligned}{c}\Delta T = \frac{{0.2}}{{55}} \times 100\% \\ = 0.364\% \\ \approx 0.4\% \end{aligned}\).

Thus, the percent uncertainty is 0.4%.

The given hand-timed measurement is:

\(\begin{aligned}{c}{T_2} = 5.{\rm{5 min}}\\{\rm{ = 5}}{\rm{.5}} \times {\rm{60}}\\{\rm{ = 330 s}}\end{aligned}\).

From equation (i), the percent uncertainty is:

\(\begin{aligned}{c}\Delta T = \frac{{0.2}}{{330}} \times 100\% \\ = 0.06\% \end{aligned}\).

Thus, the percent uncertainty is 0.06%.