An express train is moving at a constant speed of 108 km/h. What is this speed expressed in metres per second?

Introduction / Context:
Unit conversion is a fundamental skill tested in almost every quantitative aptitude exam. This question asks you to convert a speed given in kilometres per hour into an equivalent value in metres per second, which is the unit often used in physics and many train or motion based problems.

Given Data / Assumptions:

• Speed of the train = 108 km/h.
• We need to convert this speed into metres per second.
• We assume uniform motion without acceleration.

Concept / Approach:
The key relationship here is the numerical conversion between kilometres per hour and metres per second. One kilometre is 1000 metres and one hour is 3600 seconds. Therefore, 1 km/h equals 1000 / 3600 metres per second, which simplifies to 5 / 18 metres per second. Conversely, to convert from metres per second to km/h, we use the factor 18 / 5. In this problem, we multiply 108 km/h by 5 / 18 to obtain the equivalent speed in metres per second.

Step-by-Step Solution:
Step 1: Recall that 1 km/h = 5 / 18 metres per second.Step 2: Speed in metres per second = 108 * 5 / 18.Step 3: Simplify by dividing 108 by 18 to get 6.Step 4: Now compute 6 * 5 = 30.Step 5: Thus, the speed is 30 metres per second.

Verification / Alternative check:
Convert 30 metres per second back into km/h to verify.Using the reverse factor, multiply 30 by 18 / 5 to get 30 * 18 / 5 = 30 * 3.6 = 108 km/h.Since we arrive at the original speed given in the question, the conversion is correct.

Why Other Options Are Wrong:
10.8 metres per second and 18 metres per second correspond to incomplete or incorrect use of the conversion factor. The value 38.8 metres per second is too high and could come from mixing up 5 / 18 and 18 / 5. The value 24 metres per second ignores the exact factor and leads to an incorrect back-converted speed in km/h. Only 30 metres per second accurately represents 108 km/h.

Common Pitfalls:
A common mistake is to use 18 / 5 instead of 5 / 18 when converting from km/h to metres per second. Another frequent error is to forget either the 1000 metres in a kilometre or the 3600 seconds in an hour, leading to incorrect fractions such as 10 / 36 instead of 5 / 18. To avoid confusion, remember: to go from km/h to metres per second, multiply by 5 / 18; to go from metres per second to km/h, multiply by 18 / 5.

Final Answer:
The speed of 108 km/h is equal to 30 metres per second.