The average acceleration of a particle has the same value a₀ between every possible pair of instants in an interval. Its velocity must have the form:
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Question

The average acceleration of a particle has the same value a₀ between every possible pair of instants in an interval. Its velocity must have the form:

G1 Physics · Accepted Answer

For every pair t₁,t₂, [v(t₂)−v(t₁)]/(t₂−t₁)=a₀. Therefore v(t₂)−a₀t₂ = v(t₁)−a₀t₁ = constant. Hence v = a₀t + C.