In unit conversion for speed, 1 km/h (one kilometre per hour) is exactly equal to how many metres per second (m/s)?

Introduction / Context:
Speed can be expressed in different units depending on the context. In daily life, road speeds are often given in kilometres per hour, while in physics calculations, metres per second is a more convenient unit. Being able to convert between km/h and m/s quickly is a basic skill in physics and engineering. This question asks for the exact factor that converts 1 km/h into metres per second.

Given Data / Assumptions:

• 1 kilometre equals 1000 metres.
• 1 hour equals 3600 seconds.
• We want to express the speed 1 kilometre per hour in the unit metres per second.
• No approximations are required beyond integer arithmetic.

Concept / Approach:
Conversion between km/h and m/s is based purely on unit relationships. To convert 1 km/h to m/s, we substitute 1 kilometre with 1000 metres and 1 hour with 3600 seconds. The speed value is then expressed as a fraction of 1000 metres divided by 3600 seconds. Simplifying this fraction gives the conversion factor. This factor is used frequently to convert any speed from km/h to m/s by multiplication.

Step-by-Step Solution:
Step 1: Start with the given speed of 1 km/h. Step 2: Use the length conversion 1 km = 1000 m, so the numerator becomes 1000 m. Step 3: Use the time conversion 1 hour = 3600 s, so the denominator becomes 3600 s. Step 4: Write the speed as 1 km/h = 1000 m / 3600 s. Step 5: Simplify the fraction 1000 / 3600 by dividing both numerator and denominator by 200, giving 5 / 18. Step 6: Conclude that 1 km/h equals 5/18 m/s.

Verification / Alternative check:
To verify, you can reverse the conversion. Multiply 5/18 m/s by 3600 s to find the distance covered in one hour. First calculate 5/18 * 3600. Divide 3600 by 18 to get 200, then multiply 200 by 5 to get 1000 metres. Converting 1000 metres back to kilometres gives 1 kilometre. This confirms that a speed of 5/18 m/s corresponds exactly to 1 km/h, validating the conversion factor.

Why Other Options Are Wrong:
Option b, 18/5, is the inverse of the correct factor and is used when converting from m/s to km/h, not the other way around.

Option c, 5/16, does not match the precise ratio of 1000 to 3600 and would give an incorrect distance when converted back.

Option d, 16/5, is also unrelated to the exact relationship between metres, kilometres, hours and seconds.

Common Pitfalls:
Students often remember that there is a factor involving 5 and 18 but mix up whether they should multiply or divide. A helpful rule is: to convert from km/h to m/s, multiply by 5/18, and to convert from m/s to km/h, multiply by 18/5. Another mistake is to approximate without doing the exact calculation, which can lead to minor errors that matter in precise numerical problems. Practising the step by step conversion a few times helps fix the correct factor in memory.

Final Answer:
1 km/h is equal to 5/18 m/s.