College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ The speed of light is 186,000 miles per second. What is its speed in centimeters per second?

Use the following conversions:
- 5280 feet = 1 mile
- 12 inches = 1 foot
- 2.54 cm = 1 inch

A. [tex]\(3.01 \times 10^{11} \, \text{cm/s}\)[/tex]
B. [tex]\(3.15 \times 10^{10} \, \text{cm/s}\)[/tex]
C. [tex]\(2.99 \times 10^{10} \, \text{cm/s}\)[/tex]
D. [tex]\(3 \times 10^{11} \, \text{cm/s}\)[/tex]
E. [tex]\(6.06 \times 10^{12} \, \text{cm/s}\)[/tex]

Answer :

To convert the speed of light from miles per second to centimeters per second, we need to follow a step-by-step process involving unit conversions. Here's how it can be done:

1. Convert miles to feet:
- We know that 1 mile equals 5280 feet.
- Therefore, to convert 186,000 miles per second to feet per second:
[tex]\[
186,000 \, \text{miles/second} \times 5280 \, \text{feet/mile} = 982,080,000 \, \text{feet/second}
\][/tex]

2. Convert feet to inches:
- We know that 1 foot equals 12 inches.
- Therefore, to convert 982,080,000 feet per second to inches per second:
[tex]\[
982,080,000 \, \text{feet/second} \times 12 \, \text{inches/foot} = 11,784,960,000 \, \text{inches/second}
\][/tex]

3. Convert inches to centimeters:
- We know that 1 inch equals 2.54 centimeters.
- Therefore, to convert 11,784,960,000 inches per second to centimeters per second:
[tex]\[
11,784,960,000 \, \text{inches/second} \times 2.54 \, \text{cm/inch} = 29,933,798,400 \, \text{cm/second}
\][/tex]

So, the speed of light in centimeters per second is approximately [tex]\( 2.99 \times 10^{10} \)[/tex] cm/s.

Thus, the correct answer is:
[tex]\[
\boxed{2.99 \times 10^{10} \, \text{cm/s}}
\][/tex]