To cover a total distance of 90 km in 2.5 hours, what should be the average speed of a car in metres per second (m/s)?

Introduction / Context: Average speed questions are a staple of time, speed and distance topics in aptitude exams. Here, a car needs to cover 90 km in 2.5 hours, and we are asked to express the required average speed in metres per second (m/s). This demands both an understanding of how to compute average speed and how to convert from km/h to m/s accurately. Given Data / Assumptions:

• Total distance to be covered = 90 km.
• Total time allowed = 2.5 hours.
• The car is assumed to travel at a constant average speed.
• We need the answer in m/s, not in km/h.

Concept / Approach: The basic formula for average speed is: average speed = total distance / total time First we will find the average speed in kilometres per hour (km/h). After that, we will convert the result to metres per second (m/s) using the standard conversion: 1 km/h = 5 / 18 m/s Step-by-Step Solution: Step 1: Compute average speed in km/h. Distance = 90 km, time = 2.5 hours. Average speed (km/h) = 90 / 2.5. 2.5 = 5 / 2, so 90 / 2.5 = 90 * (2 / 5) = 180 / 5 = 36 km/h. Step 2: Convert 36 km/h to m/s. Speed in m/s = 36 * (5 / 18). 36 / 18 = 2, so speed = 2 * 5 = 10 m/s. Therefore, the required average speed is 10 m/s. Verification / Alternative check: We can check quickly by reversing the process. Convert 10 m/s back to km/h: speed (km/h) = 10 * (18 / 5) = 10 * 3.6 = 36 km/h. Now confirm that a car travelling at 36 km/h for 2.5 hours covers 90 km: distance = speed * time = 36 * 2.5 = 36 * (5 / 2) = 90 km. This matches the original distance, so our answer is consistent. Why Other Options Are Wrong: 12 m/s corresponds to 43.2 km/h, which would cover more than 90 km in 2.5 hours. 15 m/s corresponds to 54 km/h and would also cover a greater distance than needed. 20 m/s is 72 km/h, which is much faster and would cover 180 km in 2.5 hours. 8 m/s is 28.8 km/h, which is too slow and would cover only 72 km in 2.5 hours. Only 10 m/s exactly matches a 90 km journey completed in 2.5 hours. Common Pitfalls: A common mistake is to convert 2.5 hours into minutes or seconds unnecessarily and then mis-handle the units. Another error is to use an incorrect conversion factor between km/h and m/s, such as 18 / 5 instead of 5 / 18, which reverses the conversion. Some learners also mistakenly average speeds or times directly without using the correct formula. Here the calculation is straightforward as long as you compute 90 / 2.5 correctly and then convert units carefully. Final Answer: The car must travel at an average speed of 10 m/s to cover 90 km in 2.5 hours.