To calculate the distance traveled by light in a given amount of time, we can use the basic formula for distance, which is:
[tex]\[ \text{distance} = \text{speed} \times \text{time} \][/tex]
Given:
- The speed of light in a vacuum, [tex]\( c \)[/tex], is [tex]\( 2.99 \times 10^5 \)[/tex] kilometers per second.
- The time, [tex]\( t \)[/tex], is [tex]\( 3.6 \times 10^3 \)[/tex] seconds.
Let's plug these values into the formula:
1. First, write down the values:
- Speed of light, [tex]\( c = 2.99 \times 10^5 \)[/tex] kilometers per second
- Time, [tex]\( t = 3.6 \times 10^3 \)[/tex] seconds
2. Now, calculate the distance:
[tex]\[
\text{distance} = c \times t
\][/tex]
[tex]\[
\text{distance} = (2.99 \times 10^5) \, \text{km/s} \times (3.6 \times 10^3) \, \text{s}
\][/tex]
3. Perform the multiplication:
- Multiplying the coefficients:
[tex]\[
2.99 \times 3.6 = 10.764
\][/tex]
- Adding the exponents (since [tex]\( 10^5 \times 10^3 = 10^{(5+3)} = 10^8 \)[/tex]):
[tex]\[
10^5 \times 10^3 = 10^8
\][/tex]
4. Combine the results:
[tex]\[
\text{distance} = 10.764 \times 10^8 \, \text{km}
\][/tex]
5. Simplify the scientific notation:
[tex]\[
10.764 \times 10^8 \, \text{km} = 1.0764 \times 10^9 \, \text{km} = 1,076,400,000 \, \text{km}
\][/tex]
Therefore, the distance traveled by light in [tex]\( 3.6 \times 10^3 \)[/tex] seconds is [tex]\( 1,076,400,000 \)[/tex] kilometers.
So, the distance traveled by light in this time is [tex]\( 1,076,400,000 \)[/tex] kilometers.
