Question

How far does light travel in each time period? (a) \(1.0 \mathrm{~s}\) (b) \(1.0\) day (c) \(1.0 \mathrm{yr}\)

Short answer

The distance light travels is approximately (a) 299,792,458 meters in 1.0 second, (b) 25,902,068,371,200 meters in 1.0 day, and (c) 9,454,254,955,488,000 meters in 1.0 year.

Step-by-step solution

Understanding the Speed of Light

The speed of light in a vacuum is a universal constant approximately equal to 299,792,458 meters per second (m/s). This will be the speed value used to calculate the distance light travels in different time periods.

Calculating the Distance for 1.0 second

To find the distance light travels in 1.0 second, multiply the speed of light by the duration: distance = speed * time. Therefore, distance in meters = 299,792,458 m/s * 1.0 s.

Calculating the Distance for 1.0 day

First, convert the time from days to seconds by using the conversion factor: 1 day = 24 hours = 24 * 60 minutes = 24 * 60 * 60 seconds. Calculate the distance light travels in seconds for 1.0 day: distance in meters = 299,792,458 m/s * (24 * 60 * 60 s).

Calculating the Distance for 1.0 year

First, convert the time from years to seconds using the conversion: 1 year = 365.25 days (including leap years) * 24 hours * 60 minutes * 60 seconds. Find the distance in meters = 299,792,458 m/s * (365.25 * 24 * 60 * 60 s).

Key concepts

Universal Constants

Universal constants are fundamental physical quantities that remain constant throughout the universe. One of the most famous and integral to physics is the speed of light, denoted as 'c'. This constant is approximately equal to 299,792,458 meters per second in a vacuum, and its value is crucial in a myriad of scientific calculations and theories, including Einstein's theory of relativity. Understanding the speed of light as a constant allows us to accurately predict the behavior of light over time and distance, making it a cornerstone for calculations in astrophysics and cosmology.

It's important to note that 'c' is not just essential for traveling light; it underlies many equations and principles across physics, influencing how energy and matter interact. Considering its omnipresence in scientific calculations, it is essential for students to grasp the concept of universal constants like the speed of light, forming a basis for further learning in science and engineering disciplines.

Light Travel Distance Calculation

Calculating the distance light can travel involves using the formula 'distance = speed * time'. With light's speed being a universal constant, determining how far it travels is straightforward once you know the time interval. For a duration of 1.0 second, the distance light travels is simply the speed of light multiplied by one second, resulting in 299,792,458 meters. However, when working with time periods like days or years, the primary challenge lies in accurately converting these units into seconds before performing the multiplication.

Steps to Simplify Calculations

• Understand the unit of time given in the problem.
• Convert this time into seconds as it is essential for consistency when using the speed of light in meters per second.
• Multiply the total seconds by the speed of light to find the distance.

Using this method, we ensure that the vast distances light can cover over various timeframes are accurately computed, from the fractions of a second to multiple years.

Time Conversion

Effective calculations across different scientific disciplines often require converting time into a uniform unit. In physics problems involving light, converting time into seconds is standard practice since the speed of light is measured in meters per second. This conversion ensures compatibility when using the formula for distance. Here's how conversion typically works:

• For minutes, multiply by 60 (the number of seconds in a minute).
• For hours, multiply by 3600 (the number of seconds in an hour).
• For days, multiply by 86,400 (the number of seconds in a day).
• For years, it's 31,536,000 seconds for a common year, or 31,622,400 seconds for a leap year including the extra day.

To calculate the distance light travels in a day or a year, you convert those time periods into seconds first and then use the light speed constant to find the distance. Integrating time conversion concepts into your study routine will streamline solving a wide range of physics problems.