Question

Many highways in the United States have a speed limit of \(65 \mathrm{mi} / \mathrm{h}\). (a) Is this speed greater than, less than, or equal to \(65 \mathrm{~km} / \mathrm{h}\) ? Explain. (b) Find the speed limit in kilometers per hour that corresponds to \(65 \mathrm{mi} / \mathrm{h}\).

Short answer

(a) Greater; (b) 104.65 km/h.

Step-by-step solution

Conversion Factor

To convert miles per hour to kilometers per hour, we need to know that 1 mile is approximately 1.60934 kilometers. This conversion factor will help us change the units from miles to kilometers.

Formulate the Conversion

Start by multiplying the speed of 65 miles per hour by the conversion factor. The formula will be: \[ 65 \text{ mi/h} \times 1.60934 \text{ km/mi} \]

Perform the Calculation

Calculate the product to find the equivalent speed in kilometers per hour:\[ 65 \times 1.60934 = 104.6521 \text{ km/h} \]Thus, 65 miles per hour is approximately 104.65 kilometers per hour.

Compare Speeds

Given that 65 kilometers per hour is less than 104.65 kilometers per hour, the speed 65 miles per hour is greater than 65 kilometers per hour.

Conclusion

For part (a), the speed 65 mi/h is greater than 65 km/h. For part (b), the speed limit corresponding to 65 mi/h is 104.65 km/h.

Key concepts

Speed Limits

Speed limits are crucial for ensuring safety on roads. They help regulate the flow of traffic and minimize accidents. Different countries have varying units and standards for speed limits. In the United States, speeds are typically measured in miles per hour (mi/h). However, in many other parts of the world, like Europe, speeds are measured in kilometers per hour (km/h). Understanding how to compare and convert these speed limits is important for international travelers and drivers.

• Miles per hour (mph) in the US.
• Kilometers per hour (km/h) in most other countries.
• Conversion is key when traveling between countries with different standards.

Knowing how these speed limits translate can help avoid confusion and ensure that you remain within legal bounds while driving.

Kilometers to Miles Conversion

Converting between kilometers and miles is a common need, especially in contexts involving travel and physics. Knowing how to perform these conversions can ease calculations and improve your comprehension of speed-related problems. One mile is approximately equal to 1.60934 kilometers. Using this conversion factor enables you to convert any speed given in miles per hour to kilometers per hour and vice versa.

• 1 mile = 1.60934 kilometers.
• Conversion factor is essential for accurate calculations.
• Use this factor to switch units smoothly.

This conversion is particularly useful when you need to compare speeds given in different units. For example, comparing a speed of 65 mi/h with that in km/h accurately requires this conversion.

Mathematical Calculations

Performing accurate mathematical calculations is essential for converting units and solving physics problems effectively. When converting miles per hour to kilometers per hour, the multiplication of the speed by the conversion factor is the key step.
To convert 65 mi/h to km/h:

• Multiply: e 65 mi/h \( \times \) 1.60934 km/mi.
• Calculate: \e This results in \( 65 \times 1.60934 \approx 104.65 \text{ km/h} \).

Performing these calculations ensures that you can accurately compare and analyze speeds across different measurement systems. Always remember to double-check your operations to ensure precision.

Physics Problems

Physics often involves analyzing motion, speed, and distance. In problems where speed conversion is necessary, understanding how to accurately convert these units becomes fundamental. When dealing with physics problems:
1. Always start by identifying the units of measurement involved.
2. Use known conversion factors to interchange between units.
3. Apply your understanding of mathematics to compute accurate values. For example, when given a speed limit of 65 mi/h in a physics problem, converting it to 104.65 km/h may be essential for making the equations work in the metric system commonly used in scientific contexts. Recognizing and understanding these conversions helps in solving a variety of physics problems, from basic to complex scenarios, ensuring comprehensibility and accuracy.