What should be the average speed of a car (in metres per second) to cover a distance of 342 km in 1.9 hours?

Introduction / Context:
This question again tests the basic formula for average speed along with a unit conversion, but with slightly less friendly numbers. The candidate must compute the average speed in km/h first and then convert it carefully to m/s. Problems like this ensure fluency in handling decimal hours and prevent careless errors when dividing by non round numbers.

Given Data / Assumptions:

Distance to be covered = 342 km.
Time allowed = 1.9 hours.
We need the average speed in metres per second (m/s).
1 kilometre = 1000 metres, 1 hour = 3600 seconds.
The car is assumed to maintain the required average speed for the whole journey.

Concept / Approach:
Average speed is distance divided by time. So we first compute speed_kmph = 342 / 1.9 km/h. Then, to convert km/h to m/s, we multiply by 1000 / 3600. Doing the division 342 / 1.9 accurately is crucial. After we get the speed in m/s, we select the option that matches this value. A quick magnitude check ensures that the computed speed is realistic for a fast car on a highway.

Step-by-Step Solution:
Step 1: Compute average speed in km/h. speed_kmph = 342 / 1.9. 342 / 1.9 = 180 km/h. Step 2: Convert to m/s. speed_mps = 180 * 1000 / 3600. Compute numerator: 180 * 1000 = 180000. speed_mps = 180000 / 3600 = 50 m/s.

Verification / Alternative check:
We know that 36 km/h equals 10 m/s. Since 180 km/h is exactly 5 times 36 km/h, the corresponding speed in m/s should be 5 * 10 = 50 m/s. This proportional reasoning provides a very quick check of the conversion. Also, 342 km in 1.9 hours corresponds to a very fast car at highway speeds, and 50 m/s is consistent with 180 km/h, confirming that our computation is reasonable.

Why Other Options Are Wrong:
Option a (180 m/s) would correspond to an impossible road speed of 648 km/h. Option b (90 m/s) and option d (100 m/s) are even larger, suggesting unrealistically high speeds. They represent likely errors where someone directly uses the km/h number as m/s or multiplies incorrectly during conversion. Only 50 m/s correctly reflects the ratio 342 / 1.9 with proper unit conversion.

Common Pitfalls:
Common mistakes include miscalculating 342 / 1.9, forgetting to convert to m/s, or treating 1.9 hours as 1 hour 90 minutes which is incorrect. Also, some candidates may simply divide 342000 metres by 1.9 hours but forget to convert hours into seconds. Writing the formulas clearly and converting units step by step prevents such errors.

Final Answer:
The car must travel at an average speed of 50 m/s to cover 342 km in 1.9 hours.