A particle has speeds u and v at the two ends of a distance L. If its speeds at L/3 and 2L/3 are w₁ and w₂ respectively, then:
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A particle has speeds u and v at the two ends of a distance L. If its speeds at L/3 and 2L/3 are w₁ and w₂ respectively, then:

G1 Physics · Accepted Answer

Since v² varies linearly with x for constant acceleration, w₁² = u² + (v²−u²)/3 = (2u²+v²)/3, w₂² = u² + 2(v²−u²)/3 = (u²+2v²)/3. Adding, w₁²+w₂² = u²+v².