For a particle, the average velocity between every pair of instants in an interval has the same value V. Its position must be of the form:
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Question

For a particle, the average velocity between every pair of instants in an interval has the same value V. Its position must be of the form:

G1 Physics · Accepted Answer

For any t₁ and t₂, [x(t₂)−x(t₁)]/(t₂−t₁) = V. Hence x(t₂)−Vt₂ = x(t₁)−Vt₁ = constant. Therefore x = Vt + C.