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Chapter 1: Problem 24

Convert \(1.00 \mathrm{km} / \mathrm{h}\) to meters per second $(\mathrm{m} / \mathrm{s})$

Short Answer

Expert verified
Question: Convert 1.00 km/h to meters per second (m/s). Answer: \(\frac{5}{18} \mathrm{m/s}\)

Step by step solution

01

Convert distance units

In order to convert kilometers to meters, we need to know that there are 1000 meters in a kilometer. Therefore, to convert the speed from kilometers per hour to meters per hour, we will multiply the value by 1000. $$1.00 \mathrm{km/h} = 1.00 \times 1000 \mathrm{m/h} = 1000 \mathrm{m/h}$$
02

Convert time units

Now, we need to convert the time units from hours to seconds. We know that there are 60 minutes in an hour and 60 seconds in a minute, so there are a total of 3600 seconds in an hour. Therefore, we need to divide the value in meters per hour by 3600 to convert it to meters per second: $$1000 \mathrm{m/h} = \frac{1000}{3600} \mathrm{m/s}$$
03

Simplify the fraction

Now, simplify the fraction to get the final value in meters per second: $$\frac{1000}{3600} \mathrm{m/s} = \frac{10}{36} \mathrm{m/s} = \frac{5}{18} \mathrm{m/s}$$ So, \(1.00 \mathrm{km} / \mathrm{h}\) is equal to \(\frac{5}{18} \mathrm{m} / \mathrm{s}\).

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