Final answer:
A car speedometer with a 5.0% uncertainty reading at 90 km/h will have a speed range between 85.5 km/h and 94.5 km/h, which converts to 53.1 mi/h and 58.7 mi/h respectively using the conversion factor 1 km = 0.6214 mi. The correct option is Option A.
Step-by-step explanation:
Calculating Speedometer Uncertainty and Conversion to Miles per Hour
When a car speedometer reads 90 km/h with a 5.0% uncertainty, the range of possible speeds can be calculated as follows:
• Lower Range = 90 km/h - (5.0% of 90 km/h) = 90 km/h - 4.5 km/h = 85.5 km/h
• Upper Range = 90 km/h + (5.0% of 90 km/h) = 90 km/h + 4.5 km/h = 94.5 km/h
Now, to convert this range to miles per hour, we use the conversion factor where 1 km = 0.6214 mi:
• Lower Range in mi/h = 85.5 km/h × 0.6214 = 53.1 mi/h
• Upper Range in mi/h = 94.5 km/h × 0.6214 = 58.7 mi/h
Therefore, the correct option with the range of possible speeds both in kilometers per hour and miles per hour is Option A: 85.5 - 94.5 km/h; 53.1 - 58.7 mi/h.