Question

A particle moves according to a law of motion s = f(t), t ≥ 0, where...

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 − 15t2 + 72t

(a) Find the velocity at time t.
v(t) =

(b) What is the velocity after 5 s?

v(5) =

(c) When is the particle at rest?

t =   s (smaller value)
t =   s (larger value)

When is the particle moving in the positive direction? (Enter your answer in interval notation.)

t

Find the total distance traveled during the first 7 s.
ft

When, for

0 ≤ t < ∞,

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

When, for

0 ≤ t < ∞,

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

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