Question

body covers one third of its journey with speed U and next third with speed v and last third with speed w calculate the average speed of the body over the entire journey

Answer 1

We take the distance as '3x', so one-third distance will be 'x'. We derive time of each 'x' distance with the formula: t=d/s. We then put the values in the formula of average speed: total distance/ total time

Answer 2

Answer:

The average speed of the body over the entire journey is $v_{avg}=\dfrac{3uvw}{vw+uw+uv}$.

Explanation:

Given that,

A body covers one third of its journey with speed U and next third with speed v and last third with speed w.

Let total distance be 3x.

We need to calculate the total time

The time is equal to the distance upon speed.

$t =\dfrac{d}{v}$

When a body covers one third of its journey with speed u.

The time will be

$t_{1} =\dfrac{x}{u}$

When a body covers next third of its journey with speed v.

$t_{2} =\dfrac{x}{v}$

When a body covers next third of its journey with speed v.

$t_{3} =\dfrac{x}{w}$

Average speed :

The average speed is equal to the total distance divided by the total time.

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

Put the value into the formula

$v_{avg}=\dfrac{3x}{\dfrac{x}{u}+\dfrac{x}{v}+\dfrac{x}{w}}$

$v_{avg}=\dfrac{3uvw}{vw+uw+uv}$

Hence, The average speed of the body over the entire journey is $v_{avg}=\dfrac{3uvw}{vw+uw+uv}$.