Q19PE - College Physics (Urone)

Question

(a) If your speedometer has an uncertainty of 2.0 km/h  at a speed of  90 km/h, what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads  60  km/h , what is the range of speeds you could be going?

Step-by-Step Solution

Answer

1. The percentage uncertainty is  2.2%.
2. The range of speedometer is  59 km/h  to  61 km/h .

Step 1: Definition of percentage uncertainty

Uncertainty as a percentage is just relative uncertainty multiplied by 100. The percent uncertainty likewise lacks units since it is a ratio of comparable values.

Given Data:

Consider the given data as below.

The speed reading of speedometer is  $\mathrm{v}=90 \mathrm{km}/\mathrm{h}$.

The uncertainty of speedometer is of  $\mathrm{\delta v}=2.0 \mathrm{km}/\mathrm{h}$.

Step 2: Calculation of percentage uncertainty The percentage uncertainty is defined by

$\%\mathrm{uncertainty}=\frac{\mathrm{\delta v}}{\mathrm{v}}\times 100 .....\mathbf{.}\left(1\right)$

Substitute known values in the above equation.

$$\begin{gathered} \%\mathrm{uncertainty}=\frac{20 \mathrm{km}/\mathrm{h}}{90 \mathrm{km}/\mathrm{h}}\times 100 \\ =2.2\% \end{gathered}$$

Step 3: (b) Defining the range of the speed

Consider the given data as below.

The speed reading of the speedometer is, $\mathrm{v}=60 \mathrm{km}/\mathrm{h}$

The speedometer has the same percentage uncertainty as in the previous par. 

Rearrange equation (1), and you have

$\mathrm{\delta v}=\frac{\%\mathrm{uncertainty}\times \mathrm{v}}{100}$

Substitute known values the above equation.

$$\begin{gathered} \mathrm{\delta v}=\frac{2.2\%\times 60 \mathrm{km}/\mathrm{h}}{100} \\ =1.32 \mathrm{km}/\mathrm{h} \\ \mathbf{:}\mathbf{ }1 \mathrm{km}/\mathrm{h} \end{gathered}$$

Step 4: Deriving conclusions

1. The percentage uncertainty is  2.2%.
2. The range of speedometer is  59 km/h  to  61 km/h .