Question

A particle Travels the first half of its Total distance along a straight line with a speed V kilometre per hour then next half with a speed of 60 km per hour the average speed for the total journey is 40 kilometre per hour then value of v is

Answer 1

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Distance covered in time n/2 (1st half)40*n/2=20n

Distance coveredin time n/2 (2nd half)60*n/2=30n

Total distance =(30n+20n)=50n

Time taken=n

Average speed=50n/n=so n cuts n =50km per/h

Answer 2

Given:

• A particle travels the first half of its total distance along a straight line with a speed v km/h
• Then next half with a speed of 60 km/h
• Average speed for the total journey is 40 km/h

To Find:

Value of v

Solution:

We know that,

• If a body covers first half of a distance with speed v₁ and second half with speed v₂, then

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

$\rule{190}{1}$

Here,

v₁ is v km/h

v₂ is 60 km/h

Now, on applying above formula for the motion of given particle, we get

$\longrightarrow\rm{Average\:Speed=\dfrac{2v_{1}v_{2}}{v_{1}+v_{2}}}$

$\longrightarrow\rm{40=\dfrac{2(v)(60)}{v+60}}$

$\longrightarrow\rm{40(v+60)=120v}$

$\longrightarrow\rm{40v+2400=120v}$

$\longrightarrow\rm{2400=120v-40v}$

$\longrightarrow\rm{2400=80v}$

$\longrightarrow\rm{80v=2400}$

$\longrightarrow\rm{v=\dfrac{\cancel{2400}}{\cancel{80}}}$

$\longrightarrow\rm\green{v=30\:km/h}$

Hence, the value of v is 30 km/h.