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 − 9t2 + 15t

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

  

(b) What is the velocity after 4 s?

v(4) =  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 in interval notation.)
t   



(e) Find the total distance traveled during the first 6 s.
ft

(f) Find the acceleration at time t.
a(t) =  

  

Find the acceleration after 4 s.

a(4) =  ft/s2



(g) Graph the position, velocity, and acceleration functions for the first 6 s.


(h) 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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