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 - 12t² + 45t (a) Find the velocity at time t (in ft/s). v(t) = (b) What is the velocity (in ft/s) after 4 s? v(4)= ft/s (c) When (in seconds) is the particle at rest? (smaller value) t = S (larger value) t =
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 - 12t² + 45t (a) Find the velocity at time t (in ft/s). v(t) = (b) What is the velocity (in ft/s) after 4 s? v(4)= ft/s (c) When (in seconds) is the particle at rest? (smaller value) t = S (larger value) t =
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Q13. Please answer all the parts to this question
Transcribed Image Text: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 - 12t² + 45t
(a) Find the velocity at time t (in ft/s).
v(t) =
(b) What is the velocity (in ft/s) after 4 s?
v(4) =
ft/s
(c) When (in seconds) is the particle at rest?
(smaller value) t =
(larger value) t =
(d) When (in seconds) is the particle moving in the positive direction? (Enter your answer using interval notation.)
tE
(f)
(e) Find the total distance (in feet) traveled during the first 8 s.
a(t) =
Find the acceleration at time t (in ft/s2).
60
Find the acceleration (in ft/s2) after 4 s.
a(4) =
ft/s²
40
(g) Graph the position, velocity, and acceleration functions for the first 8 s.
y
y
20
ft
- 20
S
S
S
a
2
4
6
8
t
60
40
a
40
acc
20
2
4
6
S
20
-20
V
2
4
(h) When, for 0 ≤ t < ∞, is the particle speeding up? (Enter your answer using interval notation.)
When, for 0 < t < ∞, is it slowing down? (Enter your answer using interval notation.)
6
8
y
t
60
- 20
8
y
t
60
40
20
- 20
V
2
4
6
8
t
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