To determine which measurement is the most accurate and which one is the most precise, we need to understand the definitions of accuracy and precision:

• Accuracy refers to how close a measured value is to the true value.
• Precision refers to how close repeated measurements are to each other or how finely a measurement is specified.

Given the measurements and their descriptions:

1. A: Between 76.8 m/s and 77.2 m/s
   This measurement is provided as a range. The midpoint is $\frac{76.8 + 77.2}{2} = 77.0 \, \text{m/s}$, and the range (precision) is $\pm 0.2 \, \text{m/s}$.

2. B: 74 m/s
   This is a single value without any indication of uncertainty or range.

3. C: 75.5 m/s ± 0.70%
   The uncertainty in this measurement is $0.70\%$ of 75.5 m/s, which equals $75.5 \times 0.007 = 0.5285 \, \text{m/s}$. So, the measurement can be expressed as $75.5 \, \text{m/s} \pm 0.53 \, \text{m/s}$.

4. D: 75 m/s ± 0.1 m/s
   This measurement has a clear uncertainty, indicating it could be anywhere between $74.9 \, \text{m/s}$ and $75.1 \, \text{m/s}$.

Evaluating Accuracy:

• The most accurate measurement is the one closest to the given measurement of 76 m/s.

  • A: The midpoint is 77.0 m/s, which is $|77.0 - 76| = 1.0$ m/s away from the true value.
  • B: 74 m/s is $|74 - 76| = 2.0$ m/s away from the true value.
  • C: 75.5 m/s is $|75.5 - 76| = 0.5$ m/s away from the true value.
  • D: 75 m/s is $|75 - 76| = 1.0$ m/s away from the true value.

  Therefore, C (75.5 m/s ± 0.53 m/s) is the most accurate measurement.

Evaluating Precision:

• The most precise measurement has the smallest uncertainty or range.

  • A: The range is 0.4 m/s (± 0.2 m/s).
  • B: No precision is provided (no uncertainty).
  • C: The uncertainty is 0.53 m/s (± 0.53 m/s).
  • D: The uncertainty is 0.1 m/s (± 0.1 m/s).

  Therefore, D (75 m/s ± 0.1 m/s) is the most precise measurement.

Summary:

• Most Accurate: Measurement C (75.5 m/s ± 0.53 m/s)
• Most Precise: Measurement D (75 m/s ± 0.1 m/s)

Would you like more details or have any questions?

Here are five questions that expand on this topic:

1. How does the percentage uncertainty affect the accuracy of a measurement?
2. Why is precision important in scientific measurements?
3. Can a measurement be precise but not accurate? Explain with an example.
4. How can one reduce the uncertainty in a measurement?
5. What methods are used to determine the true value in a measurement?

Tip: Always report both the measurement and its uncertainty to provide a complete picture of your data's reliability.