A car has to cover a distance of 144 km in 3.2 hours. What average speed in metres per second should the car maintain to cover this distance on time?

Introduction / Context:

This question combines the idea of average speed with unit conversion from kilometres per hour to metres per second. The car must cover a fixed distance in a fixed time, and we are asked to express the required average speed in m/s rather than km/h. Such problems are very common in exams and also reflect how speed is measured in different contexts such as road travel and physics.

Given Data / Assumptions:

• Required distance = 144 km.
• Available time = 3.2 hours.
• We need average speed in metres per second.
• 1 km = 1 000 m and 1 hour = 3 600 s.
• Car travels at a constant average speed over the entire distance.

Concept / Approach:

The average speed in km/h is distance divided by time, both taken in kilometres and hours. Once that value is obtained, we convert it into metres per second using the standard factor 5/18. It is important to treat 3.2 hours as a decimal number of hours, equal to 3 hours and 12 minutes, but we can work directly in decimal form without converting to minutes.

Step-by-Step Solution:

Verification / Alternative check:

We can verify by converting 45 km/h directly. In one hour at 45 km/h, the car travels 45 000 metres. Dividing by 3 600 seconds in an hour gives 45 000 / 3 600 = 12.5 metres per second. This matches the value obtained using the 5/18 factor. Therefore 12.5 m/s is the correct average speed required to cover 144 km in 3.2 hours.

Why Other Options Are Wrong:

Option 10 m/s corresponds to only 36 km/h, which would be too slow to cover 144 km in 3.2 hours. Option 7.5 m/s corresponds to 27 km/h, even slower. Option 15 m/s corresponds to 54 km/h, which would cover the distance in less than 3.2 hours. Only 12.5 m/s corresponds to exactly 45 km/h, the speed that satisfies the given distance and time requirement.

Common Pitfalls:

Common mistakes include misreading 3.2 hours as 3 hours 20 minutes rather than 3 hours 12 minutes, or incorrectly computing 144 / 3.2. Some students try to convert units first and then divide, which can be more complicated. It is simpler to find the speed in km/h and then convert. Errors also occur when using the conversion factor, such as multiplying by 18/5 instead of 5/18.

Final Answer:

The car should maintain an average speed of 12.5 metres per second.