To convert \(\text{km/h}\) into \(\text{m/s}\), multiply by \(\frac{5}{18}\). To convert \(\text{m/s}\) into \(\text{km/h}\), multiply by \(\frac{18}{5}\).
Step 1: Understanding the Concept:
Unit conversion is a fundamental process in physics to ensure all parameters in an equation are in the same system of units, usually the International System of Units (SI).
Speed is commonly expressed in kilometers per hour (\( \text{km/h} \)) for vehicular speeds but needs to be in meters per second (\( \text{m/s} \)) for most kinematic calculations involving seconds or meters. Step 2: Key Formula or Approach:
To convert from \( \text{km/h} \) to \( \text{m/s} \):
1 kilometer = 1000 meters.
1 hour = 3600 seconds (60 minutes \(\times\) 60 seconds).
\[ 1 \text{ km/h} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{5}{18} \text{ m/s} \]
Therefore, to convert speed from \( \text{km/h} \) to \( \text{m/s} \), multiply the value by \( \frac{5}{18} \). Step 3: Detailed Explanation:
1. Start with the given value: \( 54 \text{ km/h} \).
2. Multiply by the conversion factor \( \frac{5}{18} \):
\[ \text{Speed in m/s} = 54 \times \frac{5}{18} \]
3. Simplify the fraction:
Notice that 54 is a multiple of 18. Specifically, \( 18 \times 3 = 54 \).
\[ \text{Speed} = 3 \times 5 = 15 \text{ m/s} \]
4. Alternatively, you can do it step-by-step:
- \( 54 \text{ km/h} = 54,000 \text{ meters per hour} \).
- \( \frac{54,000 \text{ meters}}{3600 \text{ seconds}} = \frac{540}{36} \text{ m/s} \).
- \( \frac{540}{36} = 15 \text{ m/s} \). Step 4: Final Answer:
The speed \( 54 \text{ km/h} \) is exactly equal to \( 15 \text{ m/s} \).
Thus, the correct answer is Option (C).
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