Final answer:
The student inquired about accuracy and precision in regard to time measurements with a new stopwatch. The stopwatch's ±0.05 s uncertainty affects our ability to discern the accuracy of close race outcomes, even though it provides precise measurements. As a result, the stopwatch's usefulness might be limited in closely contested sprints.
Step-by-step explanation:
The student is asking about the concepts of accuracy and precision in the context of time measurements in physics, specifically relating to a high school track coach using a new stopwatch with an uncertainty of ±0.05 s. Accuracy refers to how close a measured value comes to the actual or true value, while precision refers to how consistently you can get the same measurement under the same conditions.
- 4.01 sec - This is a precise and accurate measurement if the true time is close to 4.01 sec, considering the stopwatch's uncertainty.
- 40.1 sec - This is also precise, but its accuracy depends on the true time. If the true time is around 40.1 sec, it is accurate.
- 401.056 sec - This measurement is precise up to the millisecond, but without a true time for comparison, we can't say for certain about accuracy.
Given the stopwatch's uncertainty, the measurements are considered to have high precision. However, a slight variation of 0.08s between two timings (12.04s and 11.96s) could be within the margin of error, and so it's difficult to conclusively state whether the sprinter was truly faster during the second run.
For a closely contested race with times of 12.04s and 12.07s, the stopwatch's uncertainty could mean the difference between first and second place is not reliably measurable. Therefore, the new stopwatch may have limited helpfulness in detailed timing for closely contested sprints.