Question

Using the idea that \(1.602 \mathrm{~km}=1.000 \mathrm{mi}\), convert a speed of \(60.0 \mathrm{mi} / \mathrm{h}\) into kilometers/hour.

Short answer

60.0 mi/h is equivalent to 96.12 km/h.

Step-by-step solution

Understand the Conversion Factor

We are given that \(1.602 \text{ km} = 1.000 \text{ mi}\). This means that each mile is equivalent to 1.602 kilometers.

Define the Initial Speed

The speed we need to convert is \(60.0 \text{ mi/h}\). This means the object is traveling at 60.0 miles every hour.

Set Up the Conversion

To convert \(60.0 \text{ mi/h}\) to kilometers per hour, multiply the speed by the conversion factor: \(1.602 \text{ km/mi}\).

Perform the Calculation

Calculate the speed in kilometers per hour as follows: \[60.0 \text{ mi/h} \times 1.602 \text{ km/mi} = 96.12 \text{ km/h}\].

Conclude the Conversion

We have completed the conversion, resulting in a speed of 96.12 kilometers/hour. This gives us the equivalent speed in kilometers/hour.

Key concepts

Speed Conversion

Speed conversion is a process used to translate speed measurements from one unit to another. Often, speeds are expressed in miles per hour (mi/h) or kilometers per hour (km/h). When converting speeds, it is essential to apply the appropriate conversion factor that relates the two measurement units. This ensures that the numerical value correctly reflects the speed in the new unit system.
For instance, if a car is traveling at 60 mi/h, and you need to convert this to km/h, you must use the known conversion factor between miles and kilometers. Through this, you can express the speed in terms of a more suitable unit for your context, such as kilometers per hour for countries using the metric system.

Metric System

The metric system is an internationally recognized system of measurement. It is based on units of ten, which makes conversions and calculations easier. Common units in this system include meters for length, kilograms for mass, and liters for volume. For speed, kilometers per hour is the standard unit.
Since many countries around the world, including most of Europe, use the metric system, understanding conversions between other systems, like the imperial system used in the United States, is crucial. Tools, formulas, and conversion factors play a key role in enabling smooth transitions between these systems, allowing for clear communication and accurate calculations.

Conversion Factors

Conversion factors are numerical multipliers that are used to convert a quantity expressed in one unit to a quantity in another unit. To effectively carry out unit conversions, such as converting speeds from miles per hour to kilometers per hour, understanding conversion factors is essential.
In the given exercise, the conversion factor is supplied as 1 mile is equivalent to 1.602 kilometers. This relationship allows for a straightforward calculation to convert speeds by multiplying the known speed by this factor. It is a simple yet powerful tool that is foundational to many scientific and mathematical calculations.

Kilometers per Hour

Kilometers per hour (km/h) is a unit of speed commonly used worldwide. It tells us how many kilometers an object travels in one hour. The flexibility of this unit makes it a preferred choice in the metric system for measuring the speed of vehicles and other moving objects.
To convert speeds into kilometers per hour, as shown in the exercise, simply apply the conversion factor from miles to kilometers. In doing so, 60 mi/h becomes 96.12 km/h using the given conversion factor, which reflects the faster pace of travel in metric units. Converting to km/h provides a clear understanding of how distances are covered over time in a metric framework.