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) = 0.01t^4 − 0.03t^3
(a) Find the velocity at time t (in ft/s).
v(t) = 0.04t^3-0.09t^2
(b) What is the velocity after 2 s?
v(2) = -0.04 ft/s
(c) When is the particle at rest?
t = 0 s (smaller value)
t = 2.25 s (larger value)
(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)
[2.25, inf)
(e) Find the total distance traveled during the first 11 s. (Round your answer to two decimal places.)
ft.
h) When is the particle speeding up?
slowing down?
How do I answer part e and h

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.
f(t) = 0.01t^4 − 0.03t^3
(a) Find the velocity at time t (in ft/s).
v(t) =  0.04t^3-0.09t^2
(b) What is the velocity after 2 s?
v(2) =  -0.04  ft/s
(c) When is the particle at rest?
t =  0  s (smaller value)
t =  2.25  s (larger value)
(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)
 [2.25, inf)
(e) Find the total distance traveled during the first 11 s. (Round your answer to two decimal places.)
  ft.
h) When is the particle speeding up?
slowing down? 
How do I answer part e and h

anonymous · Answer

Distance is (f(11)-f(0))/(11-0)

anonymous · Answer

Why did you choose f(0)?

anonymous · Answer

Because s is the position function, and you start a journey at the beginning, and end when you are done =D

anonymous · Answer

f(11)=0.01(11)^4 -0.03(11)^3 right?

anonymous · Answer

Yes, and then f(0)=0. Your answer will just be f(11)

anonymous · Answer

so it would be 106.48/11 =9.68 and that is the total distance traveled

anonymous · Answer

it says that still isn't the right answer

anonymous · Answer

It may be just 106.48 feet.

anonymous · Answer

I tried that too and it said it was wrong still

anonymous · Answer

I have the way you solved it in my notes but every answer I get is wrong