Question

The average speed of helium at \(25^{\circ} \mathrm{C}\) is \(1255 \mathrm{~m} / \mathrm{s}\). Convert this speed to miles per hour (mph).

Short answer

The speed is approximately 2804.4 mph.

Step-by-step solution

Convert Temperature for Context

Although not directly needed for the conversion, knowing that the temperature given is in Celsius is useful for broader contexts. It reaffirms that the initial speed is given in metric units which need converting to Imperial units.

Convert Speed from Meters per Second to Miles per Hour

To convert the speed from meters per second to miles per hour, use the conversion factor. Given: 1 mile = 1609.34 meters, 1 hour = 3600 seconds. First, calculate how many meters make a mile: \[ rac{1255 ext{ meters}}{1 ext{ second}} imes rac{1 ext{ mile}}{1609.34 ext{ meters}} = 0.779 ext{ miles per second} \]Next, convert seconds to hours:\[0.779 ext{ miles per second} imes 3600 ext{ seconds per hour} = 2804.4 ext{ miles per hour} \]

Key concepts

Speed Conversion

Speed conversion is the process of translating speed measurements from one unit to another. Understanding this concept is crucial, especially when working with different measurement systems. Imagine driving a car. In some countries, speed is measured in kilometers per hour (kph), while in others, it's miles per hour (mph). To communicate effectively across these regions, converting between these units becomes essential.

• Identify the initial speed and unit - In our case, we're starting with meters per second (m/s).
• Choose the desired unit - We want speed in miles per hour (mph).
• Apply conversion factors - Find the necessary conversion factors from meters to miles and from seconds to hours.

Conversion factors simplify translation between units. For example, 1 mile equals 1609.34 meters. Using this method accurately converts the original speed to your desired unit without losing precision.

Metric to Imperial

Translating measurements from metric to imperial units is a common task in science, engineering, and daily life. This conversion helps bridge differences in the measurement systems used globally. While many countries primarily use the metric system, others like the United States, rely on the imperial system. Each has its unique units.

• Metric system - Includes meters, liters, and grams. It's widely used in most parts of the world.
• Imperial system - Comprises miles, gallons, and pounds. It's prevalent in the United States.

The key to converting metric to imperial is finding the correct conversion factor or multiplier. For example, converting meters to miles or liters to gallons requires accurate factors:

• 1 mile = 1609.34 meters.
• 1 meter ≈ 0.000621371 miles.

Using these conversions ensures consistency and accuracy across different systems, making global communication clearer.

Meters to Miles

When converting distances from meters to miles, understanding the relationship between these units is vital. Since 1 mile is defined as 1609.34 meters, this fixed rate facilitates conversions.

• Determine how many meters need converting — the number of meters signifies your given distance.
• Use the conversion factor — Divide the total meters by 1609.34 to get the distance in miles.

This operation is simple, yet precision is key. A miscalculated conversion factor can skew results, leading to incorrect outcomes. By carefully following steps and using calculators, one can smoothly convert meters to miles, essential in areas like athletics, travel, and logistics.

Temperature Context

While temperature does not play a direct role in speed conversions, understanding temperature context helps anchor measurements in real-world scenarios. Given in Celsius, it reminds us that speed originated from metric contexts.

Temperature affects the speed of molecules. At higher temperatures, molecules move faster, influencing measured average speeds. For instance, the average speed of gas molecules like helium depends on room temperature.

• Celsius (°C) - This scale is part of the metric system and is crucial in scientific settings.
• Fahrenheit (°F) - Used mainly in the United States, provides another perspective on temperature conditions.

When conducting experiments or interpreting scientific data, recognizing the temperature context, particularly which scale is used, ensures comprehension and lends precision to results. It frames the conditions under which initial measurements were made, providing insight into the broader impacts temperature might have on the scenario.