Question

7. Consider the following two scenarios and tell in which
wing two scenarios and tell in which case average speed is harmonic mean or arithmetic meen
Case 1: A fellow travels from city A to city B. For
travels from city A to city B. For the first hour, he drove at the constant speed of 20 km nr. When
(instantaneously) increased his speed and, for the ne
increased his speed and, for the next hour, kept it at 30 km per hour. Find the average speed
motion
Case 2: A fellow travels from city A to city B. The first h
travels from city A to city B. The first half of the way, he drove at the constant speed of 20 km per
instantaneously) increased his speed and traveled the remaining distance at 30 km per hour. Find
average speed of the motion.​

Answer 1

Answer:

Case-1 : Arithmetic Mean

Case-2 : Harmonic Mean

Explanation:

let u = 20 km/h, v = 30 km/h

Case-1 :

total distance b/w A & B = (u × 1) + (v × 1) = (u + v) km

total time = 1 + 1 = 2 h

avg speed = (u + v) / 2 ......... (A.M.)

= (20 + 30) /2 = 25 km/h

Case-2 :

let total distance = 2x km

so, total time = (x/u + x/v) h

hence,

avg speed= 2x / (x/u + x/v) = 2/(1/u + 1/v)

avg speed= 2x / (x/u + x/v) = 2/(1/u + 1/v)=2uv/(u + v) ................(H.M.)

= 2 × 20 × 30 / (20 + 30) = 24 km/h

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Hope, it helps you.