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.
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