A particle moves according to a law of motion s = f(t), t ? 0,where t is measure

Question

A particle moves according to a law of motion s = f(t), t ? 0,where t is measured in seconds and s in feet. could someone help me with the missing questions , I also dont know how to enter in interval notation thanks (d) When is the particle moving in the positive direction? (Enter your answer in interval notation.) (e) Find the total distance traveled during the first 7 s. (h) When is the particle speeding up? (Enter your answer in interval notation.) When is it slowing down? (Enter your answer in interval notation.)

Explanation / Answer

f(t) = t3 - 15t2 + 72t

v(t) = 3t2 - 30t + 72

v(t) = 3(x-6)(x-4)

particle is moving in positive direction when velocity of the particle is possitive

v is positive when t belongs to (0,4) and (6,8)

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