Question

a car trave;s a certain distance with a speed of 50km/h and returns with a speed of 40km/h . find the average speed and average velocity of car for thr whole journey.

Answer 1

Given:

A car travels a certain distance with a speed of 50 km/h and returns with a speed of 40 km/h

To Find:

The 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

$\pink{\underline{\boxed{\bf{Average\ Speed=\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}}}}}$

• Average velocity is given by

$\pink{\underline{\boxed{\bf{Average\ Velocity=\dfrac{Total\ Displacement}{Total\ Time\ Taken}}}}}$

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It is given that car travels certain distance and then return to initial position, that means distance travelled in going and returning is same.

So, journey of car in going is considered as first half and journey of car in returning is considered as second half of the total journey.

Let the average speed of car be S

So,

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

$\longrightarrow\rm{S=\dfrac{2(50)(40)}{50+40}}$

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

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

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Here,

Displacement of car is zero because after journey, car returns to its initial position  

Let the average velocity of car be V

So,

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

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

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

Hence, average speed of car is 44.44 km/h and average velocity of car is 0 km/h.

Answer 2

Answer

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Average speed =$\frac{Total \: distance}{Total \: time}$

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As the distance travelled by car is same.

Time taken car to go to distance -

$\longrightarrow$$t_1 = \frac{s}{v_1}$

$\longrightarrow$$t_2 = \frac{s}{v_2}$

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$V_{avg}= \frac{s \: + \: s}{t_1 + t_2}$

$\longrightarrow$$V_{avg} = \frac{2s}{\frac{s}{v_1} +\frac{s}{v_2} }$

$\longrightarrow$$V_{avg} = \frac{2v_1v_2}{v_1 + v_2}$

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$\implies$$V_1 = 50 km/hr$

$\implies$$V_2 = 40 km/hr$

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Substituting the value :-

$\longrightarrow$$V_{avg} = \frac{2 \times 50 \times 40}{50 + 40}$

$\longrightarrow$$V_{avg} = \frac{4000}{90} = 44.44$

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Average Velocity = $\frac{Total \: displacement}{Total \: time}$

As the train reaches the starting point again the displacement will be equal to zero.

$\longrightarrow$Displacement = 0

$\implies$Average Velocity = 0 km/hr

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Thanks