Question

Find the speed parameter of a particle that takes 2 years longer than light to travel a distance of \(6.0\) ly.

Short answer

The speed parameter of the particle is 0.75 light years per year.

Step-by-step solution

Determine the Time taken by the particle

We know that light will take 6 years to travel 6.0 light years as the speed of light is one light year per year. The particle takes 2 years longer than the light, so it takes 6+2=8 years.

Applying the formula for velocity

The formula for velocity is velocity = distance / time. Here, distance is 6 light years and time is 8 years. Substitute these into the formula and calculate the velocity.

Calculating the Velocity

Substitute the values into the velocity formula, we get velocity= 6 / 8 = 0.75 light years per year.

Key concepts

Understanding the Speed of Light

The concept of the speed of light is fundamental in physics and plays a crucial role in relativistic velocity exercises like the one provided. The speed of light, denoted by the symbol 'c', is a constant and universally accepted as 299,792,458 meters per second (approximately 186,282 miles per second) or about one light year per year. This speed represents the maximum velocity at which all conventional matter and information in the universe can travel. It's a critical component of Einstein's theory of relativity, affecting how we understand time, distance, and even the nature of the universe itself.

In the context of our exercise, knowing that light travels one light year per year offers a convenient way to understand relativistic effects and calculations involving long distances, such as those traversed by particles in space. Grasping this concept is imperative for students dealing with exercises about time dilation, distance measurement in astronomy, and the theoretical limits of speed.

Navigating the Velocity Formula

The velocity formula is a fundamental equation used to calculate the speed of an object when its distance travelled and time taken are known. Expressed simply, it is:
\[\text{velocity} = \frac{\text{distance}}{\text{time}}\]
This formula is a cornerstone in physics problems dealing with motion. For our exercise, the formula allows us to determine the speed parameter of a particle by dividing the distance travelled by the time taken.

It is important to distinguish between speed and velocity in physical terms: velocity is a vector quantity, meaning it has both magnitude and direction, while speed is scalar and indicates only magnitude. In the context of textbook problems, however, these terms are often used interchangeably when the direction is not being considered. As with any equation, careful substitution of the correct values into the velocity formula is essential for accurate calculations. Applied correctly, this formula provides a clear method for solving the problem at hand.

Time and Distance Calculations

Time and distance calculations are vital components of physics that deal with the measurement of motion. To solve problems involving these elements, like our example problem concerning a particle outpacing light by two years over a distance of six light years, a clear understanding of the relationship between time, distance, and speed is essential.

Distance refers to the total length of the path travelled by an object, while time is simply the duration over which the movement occurs. In the context of our problem, knowing that light takes one year to travel one light year allows us to deduce that it will take six years to travel six light years. When the particle takes two years longer, we add that duration to the light’s travel time, resulting in an eight-year time frame for the particle.

The ability to perform these types of calculations is imperative for students tackling exercises involving relativistic speeds and astronomical distances. Mastery of time and distance calculations builds a strong foundation for more complex physics concepts coming their way in advanced studies.