Question

Which of the following speeds is the least?

• A. \( 50 \text{ meter / second} \)
• B. \( 50 \text{ meter / minute} \)
• C. \( 70 \text{ km / hour} \)
• D. \( 5 \text{ km / minute} \)

Hint:

\textbf{Unit Conversion for Speed.} When comparing speeds given in different units, it is essential to convert them to a common unit. Common conversions include: - \( 1 \text{ km} = 1000 \text{ meters} \) - \( 1 \text{ hour} = 60 \text{ minutes} \) - \( 1 \text{ minute} = 60 \text{ seconds} \) To convert km/hour to m/s, multiply by \( \frac{1000}{3600} = \frac{5}{18} \). To convert km/minute to m/s, multiply by \( \frac{1000}{60} = \frac{50}{3} \).

Answer 1

The Correct Option is B

To compare the speeds, we need to convert them to the same units, for example, meters per second (m/s). (A) \( 50 \text{ meter / second} = 50 \text{ m/s} \) (B) \( 50 \text{ meter / minute} = \frac{50 \text{ meter}}{60 \text{ second}} = \frac{5}{6} \text{ m/s} \approx 0.83 \text{ m/s} \) (C) \( 70 \text{ km / hour} = 70 \times \frac{1000 \text{ meter}}{3600 \text{ second}} = \frac{70000}{3600} \text{ m/s} = \frac{700}{36} \text{ m/s} = \frac{175}{9} \text{ m/s} \approx 19.44 \text{ m/s} \) (D) \( 5 \text{ km / minute} = 5 \times \frac{1000 \text{ meter}}{60 \text{ second}} = \frac{5000}{60} \text{ m/s} = \frac{500}{6} \text{ m/s} = \frac{250}{3} \text{ m/s} \approx 8(C)33 \text{ m/s} \) Now, let's compare the values in m/s: (A) \( 50 \text{ m/s} \) (B) \( \approx 0.83 \text{ m/s} \) (C) \( \approx 19.44 \text{ m/s} \) (D) \( \approx 8(C)33 \text{ m/s} \) The least speed is \( \approx 0.83 \text{ m/s} \), which corresponds to \( 50 \text{ meter / minute} \). Therefore, the least speed is option (B)