Question

An oxygen molecule travels 975 miles per hour at room temperature. What is the velocity in meters per second? (Given: \(1 \mathrm{mi}=1.61 \mathrm{~km})\).

Short answer

The velocity is 436 meters per second.

Step-by-step solution

Convert miles to kilometers

First, we need to convert the speed from miles per hour to kilometers per hour using the conversion factor given: 1 mile is equal to 1.61 kilometers. So, multiply 975 miles by 1.61 kilometers per mile:\[975 \text{ miles/hour} \times 1.61 \text{ km/mile} = 1570.75 \text{ km/hour}\]

Convert kilometers per hour to meters per second

Next, we will convert the velocity from kilometers per hour to meters per second. There are 1000 meters in a kilometer and 3600 seconds in an hour. Therefore, use the conversion factors:\[1570.75 \text{ km/hour} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hour}}{3600 \text{ seconds}}\]This simplifies to:\[1570.75 \times \frac{1000}{3600} = 436.319 \text{ meters/second}\]

Round to appropriate significant figures

Looking at the number of significant figures in our initial data (975 miles per hour), we have 3 significant figures. Thus, we'll round the result to 3 significant figures:\[436.319 \rightarrow 436 \text{ meters/second}\]

Key concepts

Velocity Conversion

Velocity conversion is an important concept in physics that allows you to express the same speed in different units.
Understanding how to convert velocity accurately helps in scientific calculations as not all measurements globally use the same systems. In this exercise, the speed of an oxygen molecule is initially given in miles per hour (mph), but it needs to be converted to meters per second (m/s). This conversion process involves two key steps:

• First, convert mph to kilometers per hour (km/h) because the measurement units provided include miles and kilometers. Given that 1 mile equals 1.61 kilometers, you multiply the speed in miles per hour by this factor to get km/h.
• Second, convert km/h to m/s. This involves using the fact that there are 1000 meters in a kilometer and 3600 seconds in an hour. Thus, the velocity in km/h is multiplied by 1000/3600 to convert to m/s.

By following these steps, we can convert any velocity given in miles per hour to meters per second, allowing for consistent and accurate calculations across different scientific scenarios.

Significant Figures

Significant figures reflect the precision of a measurement. They are crucial in scientific calculations to ensure accuracy and reliability. When converting or calculating measurements, it is vital to carry the precision of the original data through the entire calculation. In our example, the original velocity of the oxygen molecule was given as 975 mph. This figure has three significant figures.

• When performing calculations, all intermediary and final results should maintain this level of precision.
• In the final step, we round our calculated velocity in m/s to the correct number of significant figures from the original data, which in this case tells us to round 436.319 m/s to three significant figures, resulting in 436 m/s.

Rounding to proper significant figures is essential because it reflects the true measurement precision, avoiding the inclusion of speculative digits.

Measurement Units

Measurement units are the backbone of any physical calculation. They define what quantity is being measured and how it is expressed. Understanding the units is crucial when performing conversions like those seen in physics problems.

• Units can belong to different systems of measurement, such as the metric system (meters, kilometers) and the imperial system (miles).
• For accurate calculations, conversions between these units are necessary. For example, in the given problem, an understanding of both the conversion from miles to kilometers and from kilometers per hour to meters per second is required.
• Using conversion factors allows the transformation from one unit to another while preserving the magnitude of the physical quantity measured, ensuring that different quantities are comparable and compatible.

Being familiar with common conversion factors can help you save time and avoid mistakes when encountering multi-unit problems, making your calculations both efficient and correct.