Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 54a

Chapter 1, Problem 54a

Using your knowledge of metric units, English units, and the information on the back inside cover, write down the conversion factors needed to convert (a) km/hr to m/s

Verified step by step guidance

Identify the units involved in the conversion: kilometers per hour (km/hr) to meters per second (m/s).

Recognize that 1 kilometer is equal to 1000 meters. This gives us the conversion factor: 1 km = 1000 m.

Understand that 1 hour is equal to 3600 seconds. This provides the conversion factor: 1 hr = 3600 s.

Set up the conversion by multiplying the given value in km/hr by the conversion factors to cancel out the original units and introduce the desired units. The expression will be: \( \text{value in km/hr} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hr}}{3600 \text{ s}} \).

Simplify the expression to find the conversion factor from km/hr to m/s, ensuring that the units of kilometers and hours cancel out, leaving meters per second as the final unit.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Metric and English Units

Metric units are part of the International System of Units (SI), which includes meters (m), kilometers (km), and seconds (s). English units, such as miles and feet, are commonly used in the United States. Understanding the differences between these systems is crucial for performing conversions accurately.

Conversion Factors

Conversion factors are ratios that express how many of one unit are equal to another unit. For example, to convert kilometers to meters, the conversion factor is 1 km = 1000 m. Using appropriate conversion factors allows for the transformation of measurements from one unit to another, ensuring consistency in calculations.

Speed Conversion

Speed is defined as the distance traveled per unit of time, typically expressed in units like kilometers per hour (km/hr) or meters per second (m/s). To convert speed from km/hr to m/s, one must recognize that 1 km = 1000 m and 1 hour = 3600 seconds, leading to the conversion factor of 1 km/hr = 1/3.6 m/s.

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