Final answer:
The percent uncertainty of a speedometer with a 2.0 km/h uncertainty at 90 km/h is 2.2%. With the same percent uncertainty at 60 km/h, the range of speeds you could be going is from 58.0 to 62.0 km/h.
Step-by-step explanation:
When dealing with measurements, understanding uncertainty is important for interpreting results. In this case, we are looking at the uncertainty of a speedometer reading.
(a) Percent Uncertainty Calculation
To calculate the percent uncertainty, the formula is:
Percent Uncertainty = (Absolute Uncertainty / Measurement) × 100%
Thus, at a speed of 90 km/h with an uncertainty of 2.0 km/h, the calculation would be:
(2.0 km/h / 90 km/h) × 100% = 2.2%
(b) Speed Range with the Same Percent Uncertainty
If the speedometer displays 60 km/h with the same percent uncertainty of 2.2%, we calculate the absolute uncertainty and then the range of speeds you could be going.
Absolute Uncertainty at 60 km/h = 2.2% of 60 km/h = 1.32 km/h
Therefore, the range of possible speeds is:
60 km/h - 1.32 km/h to 60 km/h + 1.32 km/h = 58.68 km/h to 61.32 km/h
For simplicity, we round these values to the nearest whole numbers, which gives us a range of 58.0 to 62.0 km/h.