The acceleration of a particle as it moves along a straight line is given by a = bt + c. If s = s₀ and v = v₀ when t = 0, determine the particle’s velocity and position when t = t₁. Also, determine the total distance the particle travels during this time period. Given:

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b = 2 m 3 S c = -1 m 2 S S0 = 1 m VO = 2 m S t1 = 6 s