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A point moves with uniform acceleration and v₁ , v₂ and v₃denote the average velocities in three successive intervals of time t₁ , t₂ and t₃. Which of the following relations is correct?

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V₁ - V₂ : V₂ - V₃ = t₁ - t₂ : t₂ + t₃

v₁ - v₂: v₂ - v₃ = t₁ + t₂ : t₂ + t₃·

v₁ -v₂ : v₂ - v₃ = t₁ - t₂ : t₁ - t₃

v₁ - v₂ : v₂ - v₃ = t₁ - t₂: t₂ - t₃

answer is B.

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Detailed Solution

$tanθ = \frac{v_{2} - v_{1}}{\frac{t_{1} - t_{2}}{2}} = \frac{v_{3} - v_{2}}{\frac{t_{2} - t_{3}}{2}}$
$\Rightarrow \frac{v_{1} - v_{2}}{v_{2} - v_{3}} = \frac{t_{1} - t_{2}}{t_{2} - t_{3}}$

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