Positions of a uniformly accelerated particle at four equally spaced instants are x₁, x₂, x₃ and x₄. Which relation must hold?
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Positions of a uniformly accelerated particle at four equally spaced instants are x₁, x₂, x₃ and x₄. Which relation must hold?

G1 Physics · Accepted Answer

For constant acceleration, x as a function of time is quadratic. For equally spaced time samples, the third finite difference of a quadratic is zero: x₄ − 3x₃ + 3x₂ − x₁ = 0. Therefore x₄ = 3x₃ − 3x₂ + x₁.