In basic units conversion for speed, 1 metre per second (1 m/s) is equal to how many kilometres per hour (km/h)?

Introduction / Context:
This question tests your understanding of basic unit conversion for speed, a very common topic in physics and aptitude exams. Speed is often given in metre per second (m/s) in physics problems, while in real life and competitive exams it is frequently expressed in kilometre per hour (km/h). Knowing how to convert correctly between these units helps you switch comfortably between theoretical and practical contexts.

Given Data / Assumptions:

• We are given a speed of 1 metre per second (1 m/s).
• We want to express this same speed in kilometres per hour (km/h).
• Standard metric relationships are used: 1 kilometre = 1000 metres and 1 hour = 3600 seconds.
• No approximations are made beyond these exact relationships.

Concept / Approach:
To convert a speed from m/s to km/h, we must convert metres to kilometres and seconds to hours. Because 1 kilometre has 1000 metres, we divide by 1000 when going from metres to kilometres. Because 1 hour has 3600 seconds, we multiply by 3600 when going from seconds to hours. Combining both effects gives a constant conversion factor between m/s and km/h. This factor is 3.6, so any speed in m/s can be changed to km/h by multiplying by 3.6. We then express 3.6 as a fraction to match the options.

Step-by-Step Solution:
Step 1: Start with the given speed: v = 1 m/s. Step 2: Convert metres to kilometres. Since 1 kilometre = 1000 metres, 1 metre = 1/1000 kilometre. Step 3: Convert seconds to hours. Since 1 hour = 3600 seconds, 1 second = 1/3600 hour. Step 4: Write 1 m/s in kilometre per hour form: 1 m/s = (1/1000) kilometre / (1/3600) hour. Step 5: Divide by a fraction: (1/1000) / (1/3600) = (1/1000) * (3600/1) = 3600/1000 km/h. Step 6: Simplify 3600/1000 by dividing numerator and denominator by 200: 3600/1000 = 18/5. Step 7: Therefore, 1 m/s equals 18/5 km/h.

Verification / Alternative check:
A quick mental check is to remember the standard conversion 1 m/s = 3.6 km/h. Now 3.6 can be written as 36/10, which simplifies to 18/5. This matches the detailed calculation above, confirming that 18/5 km/h is correct. Also, approximate values support this: 1 m/s is slightly more than 3 km/h, and 18/5 = 3.6, which is reasonable for walking and running speeds when compared with everyday experience.

Why Other Options Are Wrong:
5/16 is much less than 1 and would imply that 1 m/s is slower than 1 km/h, which is not reasonable. 16/5 equals 3.2 km/h, which is close but does not match the exact conversion factor of 3.6. 5/18 is about 0.277 km/h, which is far too small and clearly inconsistent with known speeds.

Common Pitfalls:
Students often mix up the direction of conversion and either multiply or divide incorrectly by 3.6. A useful memory trick is that km/h is a larger unit for distance but a larger unit for time as well, leading to the factor 3.6 between m/s and km/h. Remember that m/s to km/h always multiplies by 3.6, while km/h to m/s divides by 3.6. Writing out the unit fractions carefully, as shown, helps avoid mistakes in exams.

Final Answer:
1 metre per second is equal to 18/5 km/h.