(a) If your speedometer has an uncertainty of 2.0km/h2.0km/h at a speed of 90km/h90km/h , what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60km/h60km/h , what is the range of speeds you could be going?
Question
(a) If your speedometer has an uncertainty of 2.0km/h2.0km/h at a speed of 90km/h90km/h , what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60km/h60km/h , what is the range of speeds you could be going?
Solution
(a) The percent uncertainty can be calculated using the formula:
Percent uncertainty = (Uncertainty / Measured Value) * 100%
Here, the uncertainty is 2.0 km/h and the measured value is 90 km/h.
So, Percent uncertainty = (2.0 km/h / 90 km/h) * 100% = 2.22%
(b) If the percent uncertainty is the same at 60 km/h, we can find the range of speeds you could be going by using the formula:
Uncertainty = Percent uncertainty * Measured Value / 100%
Here, the percent uncertainty is 2.22% and the measured value is 60 km/h.
So, Uncertainty = 2.22% * 60 km/h / 100% = 1.33 km/h
Therefore, the range of speeds you could be going is 60 km/h ± 1.33 km/h, which is between 58.67 km/h and 61.33 km/h.
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