Question

A car speedometer has a 3% uncertainty. What is the range of possible speeds when it reads 70 km/h?

a.) highest and lowest km/h
b.)highest and lowest mi/h

Answer 1

(a) A 3 % uncertainty means a 3% uncertainty on the measured value.

The measured value is
`v=70 km/h`. The 3 % of this value is

`v \cdot (3)/(100)=(70 km/h)(3)/(100)=2.1 km/h`

So, the highest and lowest values are:

`v_H = 70 km/h + 3\%=70 m/h+2.1 km/h=72.1 km/h`

`v_L =70 km/h-3 \%=70 km/h-2.1 km/h=67.9 km/h`

(b) To find the highest and lowest speeds in mi/h, we need to convert
`v_H, v_L` into these units. keeping in mind that

`1 mi = 1.609 km`

we have:

`v_H=72.1 (km)/(h) \cdot (1)/(1.609 km/mi) =44.8 mi/h`

`v_L=67.9 (km)/(h) \cdot (1)/(1.609 km/mi)=42.2 mi/h`