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27 Nov 2011 23:22:18 IST

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Average velocity!

Physics

A particle completes half of its journey with uniform velocity 'u'. Then it moves with a uniform velocity 'v' through half the time required to complete the remaining half of the journey with a uniform velocity 'w' through the remaining half of the said time. Determine the average velocity.

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hemang

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Joined: 27 Dec 2010

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28 Nov 2011 18:44:16 IST

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average velocity = total displacement/time

let the total displacement be x.

for first half,

time taken = x/2u.

also vt/2 + wt/2 = x/2 if t is the time taken when he travels at v and then at w.

(v+w)t = x

t = x/(v+w).

so we are left with

[x]/[ x/(v+w) + x/2u]...

Heidi

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Joined: 28 Sep 2011

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28 Nov 2011 18:47:55 IST

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The answer is 2u (v + w) / (u + v + w)

Arjun Virmani

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Joined: 1 Jun 2009

Posts: 1294

31 Jan 2012 17:16:03 IST

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Ultimately the time taken by the particle is same...

so the avg velocity remains u.........

ans by hemang on rearrangement matches ur ans!!!

and it is also correct as (v+w = 2u)!!!

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