To cover a distance of 333 km in 2 hours by car, what should be the average speed of the car in metres per second?

Introduction / Context:
This question combines the average speed formula with a basic unit conversion from kilometres per hour to metres per second. It reflects real life travel planning, where one may know the total distance and desired time and must find the necessary speed. Such conversions are heavily tested in quantitative aptitude because they reinforce understanding of the relationships between distance, time and speed in different unit systems.

Given Data / Assumptions:

Required distance to cover = 333 km.
Available time = 2 hours.
We need the required average speed in metres per second (m/s).
1 kilometre = 1000 metres, 1 hour = 3600 seconds.
The car is assumed to maintain constant average speed over the whole journey.

Concept / Approach:
First, we find the average speed in km/h using the formula speed = distance / time. Once we have the speed in km/h, we convert it into m/s using the standard factor 5 / 18, or equivalently multiply by 1000 / 3600. Performing the calculation in two clear stages helps reduce mistakes and makes the reasoning transparent. Finally, we match the numerical value with the given options.

Step-by-Step Solution:
Step 1: Compute the average speed in km/h. speed_kmph = 333 / 2 = 166.5 km/h. Step 2: Convert km/h to m/s. We use speed_mps = speed_kmph * 1000 / 3600. So, speed_mps = 166.5 * 1000 / 3600. Compute numerator and denominator carefully: 166.5 * 1000 = 166500. Now divide: 166500 / 3600 = 46.25. Therefore, required average speed = 46.25 m/s.

Verification / Alternative check:
We know that 1 km/h is approximately 0.2778 m/s. Multiplying 166.5 km/h by about 0.28 should give roughly 46.6 m/s, which is very close to 46.25 m/s. The slight difference is due to rounding 0.2778 to 0.28. This quick mental check confirms that our detailed computation is consistent and the order of magnitude is reasonable for a high but not impossible highway speed.

Why Other Options Are Wrong:
Option a (166.5) is the speed in km/h, not in m/s. Options c (83.25) and d (92.5) correspond to incorrect conversions or misapplied factors and would represent unrealistically high speeds in m/s. They stem from mistakes such as multiplying instead of dividing by 3.6. Only 46.25 correctly reflects the conversion from 166.5 km/h to m/s.

Common Pitfalls:
Frequent errors include forgetting to convert hours into seconds, using 60 instead of 3600, or stopping after finding the speed in km/h and directly marking it as the answer. Some students also mix up the conversion and multiply by 3600 / 1000 rather than 1000 / 3600. Always write the step as (km/h) * (1000 m / 1 km) * (1 h / 3600 s) and cancel units to confirm that the final unit is m/s.

Final Answer:
Thus, the car must travel at an average speed of 46.25 m/s to cover 333 km in 2 hours.