To determine the distance covered by a car moving with a uniform speed of [tex]\(15.0 \, m/s\)[/tex] over a period of 12.0 minutes, we need to follow these steps:
1. Convert the time from minutes to seconds:
We know that 1 minute equals 60 seconds.
[tex]\[
\text{Time in seconds} = 12.0 \, \text{minutes} \times 60 \, \text{seconds/minute} = 720 \, \text{seconds}
\][/tex]
2. Calculate the distance covered in meters:
The formula for distance when speed and time are known is:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
Given the speed is [tex]\(15.0 \, m/s\)[/tex] and the time is [tex]\(720 \, \text{seconds}\)[/tex]:
[tex]\[
\text{Distance in meters} = 15.0 \, m/s \times 720 \, \text{seconds} = 10800 \, \text{meters}
\][/tex]
3. Convert the distance from meters to kilometers:
We know that 1 kilometer equals 1000 meters.
[tex]\[
\text{Distance in kilometers} = \frac{10800 \, \text{meters}}{1000 \, \text{meters/kilometer}} = 10.8 \, \text{kilometers}
\][/tex]
4. Identify the correct option:
Among the provided options:
- [tex]\(1.02 \times 10^{-3} \, \text{km} = 0.00102 \, \text{km}\)[/tex]
- [tex]\(1.80 \times 10^{-1} \, \text{km} = 0.180 \, \text{km}\)[/tex]
- [tex]\(8.00 \times 10^{-5} \, \text{km} = 0.00008 \, \text{km}\)[/tex]
- [tex]\(1.08 \times 10^1 \, \text{km} = 10.8 \, \text{km}\)[/tex]
The correct option is:
[tex]\[
1.08 \times 10^1 \, \text{km}
\][/tex]
Thus, the distance covered by the car in 12.0 minutes is [tex]\(10.8 \, \text{kilometers}\)[/tex].
