A particle moves according to a law of motions=f(t),t0,wheretis measured in seconds andsin feet.

f(t) = 0.01t⁴0.06t³

(a) Find the velocity at timet(in ft/s). v(t) =

0.04t30.18t2

(b) What is the velocity after5s? v(5) = 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.)

(4.5,)

(e) Find the total distance traveled during the first12s. (Round your answer to two decimal places.) ft (f) Find the acceleration at timet(in ft/s²).

a(t) =

0.12t20.36t

Find the acceleration after5s.

a(5) = ft/s²

(g) Graph the position, velocity, and acceleration functions for the first12s.

(h) When, for

0t<,

is the particle speeding up? (Enter your answer using interval notation.)

When, for

0t<,

is it slowing down? (Enter your answer using interval notation.)