Question

a car travels A certain distance at a speed of 50 kilometre per hour and returns with a speed of 40 kilometres per hour calculate the average speed and average velocity of car for the whole journey

Answer 1

Given:

Speed of car during departure,v₁= 50 km/h

Speed of car during returning,v₂= 40 km/h

To Find:

Average speed and average velocity of car for the whole journey

Solution:

We know that,

• If a body covers first half of a distance with speed v₁ and second half with speed v₂, then average speed of body S is given by,

$\pink{\boxed{\bf{S=\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}}}}$

• Average velocity V is given by

$\purple{\boxed{\bf{V=\dfrac{Total\ Displacement}{Total\ Time\ Taken}}}}$

$\rule{190}{1}$

Since, distance covered by car in going and returning is same, so both the path can be considered as half of whole journey.

Let the average speed of car be S

So,

$\longrightarrow\rm{S=\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}}$

$\longrightarrow\rm{S=\dfrac{2\times50\times40}{50+40}}$

$\longrightarrow\rm{S=\dfrac{4000}{90}}$

$\longrightarrow\rm\green{S=44.44\ km/h}$

$\rule{190}{1}$

Let the average velocity be V

Now, from the question it is clear that total displacement is 0 km because car has returned to its initial position

So,

$\longrightarrow\rm{V=\dfrac{Total\ Displacement}{Total\ Time\ Taken}}$

$\longrightarrow\rm{V=\dfrac{0}{Total\ Time\ Taken}}$

$\longrightarrow\rm\green{V=0\ km/h}$

$\rule{190}{1}$

Diagram:

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Answer 2

Explanation:

average speed-here the distances are equal,we have the formula of finding average speed when distance is equal as V1*V2/V1+V2. if we substitute the values here we get 50*40/50+40 which gives 200/90=20/9 kmph which when converted into m/s gives 8.

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