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A particle moves according to a law of motion s = f(t), t ? 0, where t is measured in seconds and s in feet. f(t) = 0.01t4 ? 0.02t3 (a) find the velocity at time t (in ft/s). v(t) = .04t3?.06t2 (b) what is the velocity after 1 second(s)? v(1) = -.02 ft/s (c) when is the particle at rest? t = s (smaller value) t = s (larger value) (d) when is the particle moving in the positive direction? (enter your answer using interval notation.) (e) find the total distance traveled during the first 12 seconds. (round your answer to two decimal places.) ft (f) find the acceleration at time t (in ft/s2). a(t) = find the acceleration after 1 second(s). a(1) = ft/s2


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