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Chapter 3: Problem 2

Miles per hour. You car speedometer is showing both \(\mathrm{km} / \mathrm{h}\) and mph, miles per hour. I mile is \(1609.34 \mathrm{~m}\). (a) If your speedometer is showing \(70 \mathrm{~km} / \mathrm{h}\). What does it show in \(\mathrm{mph}\) ? (b) If your speedometer is showing \(55 \mathrm{mph}\). What does it show in \(\mathrm{km} / \mathrm{h}\) ?

Short Answer

Expert verified
70 km/h is 43.5 mph, and 55 mph is 88.5 km/h.

Step by step solution

01

Convert km/h to m/s

To convert kilometers per hour (km/h) to meters per second (m/s), use the conversion factor: 1 km/h = 0.27778 m/s. Calculate the speed in m/s: \(70 \text{ km/h} = 70 \times 0.27778 \text{ m/s} = 19.4446 \text{ m/s}\).
02

Convert m/s to miles per hour (mph)

Use the fact that 1 mile is 1609.34 meters. To convert meters per second back to miles per hour, use the conversion factor: 1 m/s = 2.23694 mph. Calculate the speed in mph: \(19.4446 \text{ m/s} = 19.4446 \times 2.23694 \text{ mph} = 43.497 mph\).
03

Summary of part (a)

The speed of 70 km/h is equivalent to 43.5 mph.
04

Convert mph to m/s

To convert miles per hour (mph) to meters per second (m/s), use the conversion factor: 1 mph = 0.44704 m/s. Calculate the speed in m/s: \(55 \text{ mph} = 55 \times 0.44704 \text{ m/s} = 24.587 m/s\).
05

Convert m/s to km/h

Use the fact that 1 kilometer is 1000 meters. To convert meters per second back to kilometers per hour, use the conversion factor: 1 m/s = 3.6 km/h. Calculate the speed in km/h: \(24.587 \text{ m/s} = 24.587 \times 3.6 \text{ km/h} = 88.5132 \text{ km/h}\).
06

Summary of part (b)

The speed of 55 mph is equivalent to 88.5 km/h.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Unit Conversion
Unit conversion is an essential skill in mathematics and science that allows you to transform quantities from one measurement system to another. It ensures that we can compare and understand measurements that might initially appear different. In this exercise, we're converting speeds between kilometers per hour (km/h), meters per second (m/s), and miles per hour (mph). The process typically involves using conversion factors, which are specific numbers that when multiplied by the original unit, change it into the desired unit. For example, to convert km/h to m/s, we use the factor 0.27778.
Kilometers per Hour to Miles per Hour
To convert speeds from kilometers per hour (km/h) to miles per hour (mph), we often break the process into smaller steps to make it easier to understand. First, you can convert km/h to meters per second (m/s) using the conversion factor: 1 km/h = 0.27778 m/s. For instance, converting 70 km/h to m/s results in:

70 km/h × 0.27778 m/s = 19.4446 m/s.

Next, you convert m/s to mph. Knowing that 1 mile is 1609.34 meters, use the conversion factor: 1 m/s = 2.23694 mph. So,

19.4446 m/s × 2.23694 mph ≈ 43.5 mph.

Thus, a speed of 70 km/h is equivalent to about 43.5 mph.
Meters per Second
Meters per second (m/s) is a standard unit of speed in the International System of Units (SI). Converting other units of speed to m/s can help in understanding and comparing speeds in a consistent way. For example, converting miles per hour (mph) to m/s involves using the conversion factor: 1 mph = 0.44704 m/s. So,

55 mph × 0.44704 m/s ≈ 24.587 m/s.

To convert this back to km/h, knowing that 1 m/s = 3.6 km/h, we calculate:

24.587 m/s × 3.6 km/h ≈ 88.5 km/h.

Thus, a speed of 55 mph is equivalent to about 88.5 km/h. Converting speeds through m/s helps in maintaining accuracy and consistency between different unit systems.

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Most popular questions from this chapter

Acceleration of gravity. The acceleration of gravity is approximately \(g=\) \(9.8 \mathrm{~m} / \mathrm{s}^{2}\) (a) Find the acceleration of gravity in feet per second squared, \(\mathrm{ft} / \mathrm{s}^{2} .1 \mathrm{foot}\) is \(0.3048 \mathrm{~m}\). (b) Find the acceleration of gravity in kilometers per hour squared, \(\mathrm{km} / \mathrm{h}^{2}\).

Ruler length. You have a platinum-iridium ruler that you have measured to be \(0.11236 \mathrm{~m}\) using a high precision method. You use the ruler to measure the length of your desk, and find that the ruler fits about 20 times across the desk. What is the length of your desk?

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