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) = t³ - 12t² + 36t (a) Find the velocity at time t. v(t) = 31² - 24t+36 (b) What is the velocity after 5 s? v(5) = -9 ft/s (c) When is the particle at rest? 2 t = 6 s (smaller value) s (larger value) (d) When is the particle moving in the positive direction? (Enter your answer in interval notation.) te (e) Find the total distance traveled during the first 7 s. ft (f) Find the acceleration at time t. a(t)=

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