College Physics Problem 1.13

(a) A car speedometer has a  5.0% uncertainty. What is the range of possible speeds when it reads 90km/h?
(b) Convert this range to miles per hour. (1km=0.6214 mi)

SOLUTIONS:

a) The uncertainty in the velocity of the car is computed as 

delta_{v}=frac{5.0%}{100%}times90.0 km/h

delta_{v}=4.5 km/h

Therefore, the range of the possible speeds is 

Range=90.0pm4.5km/hRange=85.5--94.5 km/h

 

So the range of the possible speeds is 85.5 km/hr to 94.5 km/hr

 

b) Convert the range to mi/h

For 85.5 km/hr

85.5 km/hr=frac{85.5km}{hr}timesfrac{0.6214 mi}{1 km}

85.5 km/hr=53.13 mi/hr

For 94.5 km/hr

94.5 km/h=frac{94.5km}{hr}timesfrac{0.6214 mi}{1 km}

94.5  km/h=58.72  mi/hr

Therefore, the range can be represented as 53.13 mi/hr to 58.72 mi/hr.

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