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Q.

As shown in the figure , a particle is moving with constant speed $V = π$ m/s. Considering its motion from A to B, the magnitude of the average velocity is :

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a

$\sqrt{3}$ m/s

b

$π$ m/s

c

1.5 $\sqrt{3}$ m/s

d

2 $\sqrt{3}$ m/s

answer is C.

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Detailed Solution

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Displacement $= 2 Rsin (\frac{θ}{2}) = 2 Rsin 60^{\circ} = \sqrt{3} R$
Distance (l) $= \frac{2 πR}{3} [∵ θ = \frac{ℓ}{R} \frac{2 π}{3} = \frac{ℓ}{R}]$
Time $(t) = \frac{l}{v}$
Time $(t) = \frac{2 πR}{3 π} = \frac{2 R}{3}$
Average velocity $= \frac{\sqrt{3} R}{\frac{2 R}{3}}$
$⟨ v ⟩ = \frac{3 \sqrt{3}}{2} = 1.5 \sqrt{3} m / s$

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As shown in the figure , a particle is moving with constant speed V=π m/s. Considering its motion from A to B, the magnitude of the average velocity is :