A particle moving with constant acceleration has displacements S₁ and S₂ in two successive equal time intervals τ. Its velocity exactly at the common boundary of these intervals is:
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A particle moving with constant acceleration has displacements S₁ and S₂ in two successive equal time intervals τ. Its velocity exactly at the common boundary of these intervals is:

G1 Physics · Accepted Answer

Let the velocity at the common boundary be V. For constant acceleration, average velocity over an interval equals velocity at its midpoint. Alternatively, if the first interval is 0→τ, S₁ = uτ + aτ²/2, S₂ = (u+aτ)τ + aτ²/2. Adding, S₁+S₂ = 2uτ + 2aτ² = 2τ(u+aτ) = 2τV. Hence V = (S₁+S₂)/(2τ).