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?

a) (a) 2.22% (b) 40 - 140 km/h (c) 28.6 - 151.4 km/h (d) 30 - 150 km/h
b) (a) 2.22% (b) 40 - 140 km/h (c) 28.6 - 151.4 km/h (d) 30 - 150 km/h

Answer 1

(a) The percent uncertainty in the speedometer reading at 90 km/h is 2.22%.

(b) The range of speeds at 60 km/h with the same percent uncertainty is 30 - 150 km/h.

Step-by-step explanation:

(a): The percent uncertainty in the speedometer reading is calculated using the formula:

`\[ \text{Percent Uncertainty} = \left( \frac{\text{Uncertainty}}{\text{Speed}} \right) * 100 \]`

For the given values in the question
`(\( \text{Uncertainty} = 2.0 \, \text{km/h} \) and \( \text{Speed} = 90 \, \text{km/h} \))`, the percent uncertainty is calculated as follows:

`\[ \text{Percent Uncertainty} = \left( \frac{2.0 \, \text{km/h}}{90 \, \text{km/h}} \right) * 100 \approx 2.22\% \]`

This provides the answer for part (a), which is \( 2.22\% \).

(b) To find the range of speeds at 60 km/h with the same percent uncertainty, we use the formula:

`\[ \text{Range of Speeds} = \left( \text{Speed} \pm \text{Percent Uncertainty} * \text{Speed} \right) \]`

Substituting the values
`(\( \text{Speed} = 60 \, \text{km/h} \) and \( \text{Percent Uncertainty} = 2.22\% \))`, we get:

`\[ \text{Range of Speeds} = \left( 60 \, \text{km/h} \pm (2.22\% * 60 \, \text{km/h}) \right) \]`

Solving this expression gives a range of speeds from 30 km/h to 150 km/h. The lower limit is found by subtracting the uncertainty from the speed, and the upper limit is found by adding the uncertainty to the speed. Therefore, the final answer for part (b) is \( 30 - 150 \, \text{km/h} \).