Question

(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. (1 km=0.6214 mi)

Answer 1

(a). 90±45 km/hr

(b). 55.926 ± 2.7963 mil/hr

Step-by-step explanation:

Given that,

Uncertainty = 5.0%

`\delta A=(5)/(100)`

Here, A = 90 km/h

(a). We need to calculate the range of speed

We need to calculate the error of 5.0% uncertainty

`\delta A=(5)/(100)*90`

Here,
`\delta A` = uncertainty

`\delta A=4.5\ km/h`

(b). We need to convert this range to miles per hour

1 km = 0.6214 mil

`90\ km/h=90*0.6214`

`90\ km/h=55.926\ mil/hr`

`4.5\ km/h = 4.5* 0.6214`

`4.5 km/h=2.7963\ mil/hr`

Hence, This is the required solution.

Answer 2

a) 90 ± 4.5 km/h

b) 55.926 ± 2.7963 mi/h

Step-by-step explanation:

The error of 5 % uncertainty would be

`(5)/(100)* 90=4.5`

Range of possible speeds is 90 ± 4.5 km/h

First convert 90 km/h to mi/h

1 km/h = 0.6214 mi/h

90 km/h = 90×0.6214

⇒90 km/h = 55.926 mi/h

Convert 4.5 km/h to mi/h

4.5 km/h = 4.5×0.6214

⇒4.5 km/h = 2.7963

Range of possible speeds is 55.926 ± 2.7963 mi/h