NCERT Solutions for Class 9 Science Chapter 8
Motion
NCERT Books for Session 2022-2023
CBSE Board and UP Board
Exercises Questions
Page No-112
Questions No-3
Abdul, while driving to school, computes the average speed for his trip to be 20 km/h. On his return trip along the same route, there is less traffic and the average speed is 30 km /h. What is the average speed for Abdul’s trip?
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Let one side distance = x km.
Time taken for forward trip at a speed of 20 km/h = Distance / Speed = x/20 h.
Time taken in return trip at a speed of 30 km/h = x/30 h.
Total time for the whole trip =𝑥/20+𝑥/30=3𝑥+2𝑥/60=5𝑥/60 h.
Total distance covered = 2x km.
We know, Average speed = Total distance ÷ Total time
= 2x ÷ (5x/60) = 24 kmh⁻¹.
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Given:
– Speed during the trip to school = 20 km/h
– Speed during the return trip = 30 km/h
To determine the overall average speed, we use the formula:
Total average speed = Total distance / Total time
Assuming Abdul travels the same distance to and from school:
Calculation:
Let’s denote the distance to school as ‘D’.
– Time taken for the trip to school = Distance to school / Speed to school = D / 20
– Time taken for the return trip = Distance to school / Speed of return = D / 30
The total time for the entire trip:
Total time = Time to school + Time for return trip
Total time = D / 20 + D / 30
Now, the formula for total average speed:
Total average speed = Total distance / Total time
Substituting the expression for total time:
Total average speed = 2D / (D / 20 + D / 30)
Simplify the equation:
Total average speed = 2D / ((3D + 2D) / 60)
Total average speed = 2D / (5D / 60)
Total average speed = 120 / 5
Total average speed = 24 km/h
Hence, Abdul’s average speed for his entire round trip, accounting for both the journey to school and the return trip, is calculated to be 24 km/h. This indicates that considering his varying speeds in both directions, Abdul maintained an average speed of 24 km/h throughout the entire journey.