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 0.05t³

(a) Find the velocity at time t (in ft/s).

(b) What is the velocity after 3 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 9 s. (Round your answer to two decimal places.)

(f) Find the acceleration at time t (in ft/s²).

(g) Find the acceleration after 3 s.

(h) When, for 0 t < , is the particle speeding up? (Enter your answer using interval notation.)

(i) When, for 0 t < , is it slowing down? (Enter your answer using interval notation.)