Question

A body covers one third of the distance with a velocity v1, the second one third of the distance with a velocity v2 and the remaining distance with a velocity v3, then average speed of journey is? Please give a detailed answer.

Answer 1

average speed = total distance covered /total time taken

let the total distance =3x

time taken to cover first one third (x) = t1 = x/v1

time taken to cover second one third =t2= x/v2

time taken to cover 3rd one third = t3= x/v3

average speed = 3x/(x/v1 +x/v2+x/v3)

Answer 2

Answer:

The average speed of journey is $v_{avg}=\dfrac{3v_{1}v_{2}v_{3}}{v_{2}v_{3}+v_{1}v_{3}+v_{1}v_{3}}$.

Explanation:

Given that,

A body covers one third of the distance with a velocity v₁.

The second one third of the distance with a velocity v₂

and the remaining distance with a velocity v₃.

Let the total distance is x.

A body traveled $\dfrac{x}{3}$ with velocity v₁,

So, time taken is

$t_{1}=\dfrac{x}{3v_{1}}$.....(I)

A body traveled next  $\dfrac{x}{3}$ with velocity v₂ ,

So, time taken is

$t_{2}=\dfrac{x}{3v_{2}}$.....(II)

A body traveled next  $\dfrac{x}{3}$ with velocity v₃ ,

So, time taken is

$t_{3}=\dfrac{x}{3v_{3}}$.....(II)

Now, The total time is

$T =\dfrac{x}{3v_{1}}+\dfrac{x}{3v_{2}}+\dfrac{x}{3v_{3}}$

The average speed is defined ads,

$v_{avg}=\dfrac{D}{T}$

Where, D = total distance

T = Total time

The average speed of journey is

$v_{avg}=\dfrac{3x}{\dfrac{x}{3v_{1}}+\dfrac{x}{3v_{2}}+\dfrac{x}{3v_{3}}}$

$v_{avg}=\dfrac{3v_{1}v_{2}v_{3}}{v_{2}v_{3}+v_{1}v_{3}+v_{1}v_{3}}$

Hence, The average speed of journey is $v_{avg}=\dfrac{3v_{1}v_{2}v_{3}}{v_{2}v_{3}+v_{1}v_{3}+v_{1}v_{3}}$.