A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s in feet. f(t) = t3 - 12t2 + 36t (a) Find the velocity at time t. v(t) = 37 - 24t + 36 (b) What is the velocity after 4 s? v(4) = -12 ft/s (c) When is the particle at rest? (Enter your answer as a comma-separated list.) t = 2, 6 (d) When is the particle moving in the positive direction? (Enter your answer in interval notation.) [2, 6] t = Find the total distance traveled during the first 8 s. ft (f) Draw a diagram to illustrate the motion of the particle. t = 4 t = 8 s = 4 s = 32 t = 3 t = 6 S = 0 s = 0 t = 1 t = 2 t = 0 s = 4 t = 0 s = 32 S = 0 S = 0 t = 4 t = 8 S = -4 S = - 32 t = 3 t = 6 s= 0 s = 0 t = 1 t = 2 S = -4 t = 0 S = -32 t = 0 s = 0 S= 0 S S
A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s in feet. f(t) = t3 - 12t2 + 36t (a) Find the velocity at time t. v(t) = 37 - 24t + 36 (b) What is the velocity after 4 s? v(4) = -12 ft/s (c) When is the particle at rest? (Enter your answer as a comma-separated list.) t = 2, 6 (d) When is the particle moving in the positive direction? (Enter your answer in interval notation.) [2, 6] t = Find the total distance traveled during the first 8 s. ft (f) Draw a diagram to illustrate the motion of the particle. t = 4 t = 8 s = 4 s = 32 t = 3 t = 6 S = 0 s = 0 t = 1 t = 2 t = 0 s = 4 t = 0 s = 32 S = 0 S = 0 t = 4 t = 8 S = -4 S = - 32 t = 3 t = 6 s= 0 s = 0 t = 1 t = 2 S = -4 t = 0 S = -32 t = 0 s = 0 S= 0 S S
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please do (e) and (f)
![A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s in feet.
f(t) = t3 - 12t2 + 36t
(a) Find the velocity at time t.
v(t) = 31 –
24t + 36
(b) What is the velocity after 4 s?
v(4) = |-12
ft/s
(c) When is the particle at rest? (Enter your answer as a comma-separated list.)
t = 2,6
(d) When is the particle moving in the positive direction? (Enter your answer in interval notation.)
[2, 6]
t =
(e) Find the total distance traveled during the first 8 s.
ft
(f) Draw a diagram to illustrate the motion of the particle.
t = 4
t = 8
s = 4
s = 32
t = 3
t = 6
S= 0
S= 0
t = 1
t = 2
t = 0
S= 4
t = 0
s = 32
s = 0
S = 0
S
S
t = 4
t = 8
s = -4
S= -32
t = 3
t = 6
S = 0
S = 0
t = 1
t = 2
S = -4
t = 0
S = -32
t = 0
S = 0
S = 0
S
S](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a91dce2-7b78-488c-a950-bff9db4e775f%2F63f6a0f6-3998-4b68-968a-7a638823b504%2Fcs00o0i_processed.png&w=3840&q=75)
Transcribed Image Text:A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s in feet.
f(t) = t3 - 12t2 + 36t
(a) Find the velocity at time t.
v(t) = 31 –
24t + 36
(b) What is the velocity after 4 s?
v(4) = |-12
ft/s
(c) When is the particle at rest? (Enter your answer as a comma-separated list.)
t = 2,6
(d) When is the particle moving in the positive direction? (Enter your answer in interval notation.)
[2, 6]
t =
(e) Find the total distance traveled during the first 8 s.
ft
(f) Draw a diagram to illustrate the motion of the particle.
t = 4
t = 8
s = 4
s = 32
t = 3
t = 6
S= 0
S= 0
t = 1
t = 2
t = 0
S= 4
t = 0
s = 32
s = 0
S = 0
S
S
t = 4
t = 8
s = -4
S= -32
t = 3
t = 6
S = 0
S = 0
t = 1
t = 2
S = -4
t = 0
S = -32
t = 0
S = 0
S = 0
S
S
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