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A particle travels the first half of its total distance along a straight line with a speed
‘v’ kmph and the next half, with a speed of 60kmph. If the average speed for the journey is 40kmph, the value of ‘v’ is

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detailed solution

Correct option is B

Given that a particle starts at A and reaches B

Let AB = s

C is the midpoint of AB

It is said to travelled from AC with speed $= v_{1}$ $= v$

And C to B with speed $= v_{2}$

We know $V_{Avg} = \frac{{2v}_{1} v_{2}}{v_{1} + v_{2}}$

(when body travels equal distances with different velocities)

$40 = \frac{2 v (60)}{v + 60}$

$(v + 60) 40 = 120 v$

$40v + 2400 = 120v$

$2400=120v - 40v$

$2400 = 80v$

$v = \frac{2400}{80} = 30$

$v = 30 kmph$

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2023 | www.infinitylearn.com

A particle travels the first half of its total distance along a straight line with a speed ‘v’ kmph and the next half, with a speed of 60kmph. If the average speed for the journey is 40kmph, the value of ‘v’ is