A plane travels a distance of 1800 kilometres in 5 hours along a straight route. Using the basic speed formula and converting units appropriately, what is the average speed of the plane expressed in metres per second?

Introduction / Context:
This problem checks understanding of the basic relationship between distance, time, and speed and the ability to convert speed from kilometres per hour to metres per second. Such questions are very common in quantitative aptitude tests and help reinforce the conversion factor between these two units of speed.

Given Data / Assumptions:

Total distance travelled by the plane = 1800 kilometres.
Total time taken for the journey = 5 hours.
The route is straight and the speed is assumed to be constant over the whole journey.
We are required to express the final speed in metres per second, not in kilometres per hour.
Use the standard conversion 1 kilometre = 1000 metres and 1 hour = 3600 seconds.

Concept / Approach:
The basic formula is speed = distance / time. First, we find the average speed in kilometres per hour by dividing the total distance by total time. Then we convert this value into metres per second. To convert from km/h to m/s, multiply the km/h value by 1000 and divide by 3600, which simplifies to dividing by 3.6. This two step approach gives a precise and reliable answer.

Step-by-Step Solution:
Step 1: Compute the speed in kilometres per hour: speed_kmph = distance / time = 1800 / 5 = 360 km/h. Step 2: Use the conversion relationship 1 km/h = 1000 metres / 3600 seconds = 1 / 3.6 m/s. Step 3: Convert 360 km/h to m/s: speed_mps = 360 / 3.6. Step 4: Evaluate 360 / 3.6 = 100, so the average speed is 100 metres per second. Step 5: Therefore, the plane moves at an average speed of 100 m/s over the entire journey.

Verification / Alternative check:
As a quick check, convert the total distance directly into metres and divide by the total time in seconds. Distance = 1800 km = 1800 * 1000 = 1800000 metres. Time = 5 hours = 5 * 3600 = 18000 seconds. Then speed = 1800000 / 18000 = 100 metres per second. This direct method confirms the result obtained using the conversion of km/h to m/s.

Why Other Options Are Wrong:
A value of 200 m/s would correspond to a much higher distance for the same time or a much shorter duration, which is not given. Values of 10 m/s or 20 m/s are too small; they would imply the plane travels only 180 or 360 kilometres in 5 hours. The value 50 m/s is exactly half of the correct speed and comes from incorrectly dividing by 7.2 instead of 3.6. Only 100 m/s matches both unit conversion and the given journey data.

Common Pitfalls:
Common mistakes include forgetting to convert hours into seconds, using 60 instead of 3600, or inverting the conversion factor. Some learners also accidentally multiply by 3.6 instead of dividing by 3.6 when converting from km/h to m/s. Keeping the relation straight, that km/h is a larger unit of speed than m/s for the same magnitude, helps to remember that numerical values decrease when converting from km/h to m/s.

Final Answer:
The average speed of the plane is 100 metres per second.