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 + 36t (a) Find the velocity at time t. v(t) = (b) What is the velocity after 5 s? v(5) = ft/s (c) When is the particle at rest? t t = s (smaller value) s (larger value)
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 + 36t (a) Find the velocity at time t. v(t) = (b) What is the velocity after 5 s? v(5) = ft/s (c) When is the particle at rest? t t = s (smaller value) s (larger value)
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...
Related questions
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 + 36t
(a) Find the velocity at time t.
v(t) =
(b) What is the velocity after 5 s?
v(5) =
ft/s
(c) When is the particle at rest?
t =
s (smaller value)
s (larger value)
t =
(d) When is the particle moving in the positive direction? (Enter your answer in interval notation.)
tE
(e) Find the total distance traveled during the first 7 s.
ft
(f) Find the acceleration at time t.
a(t) =
Find the acceleration after 5 s.
a(5) =
ft/s²
(g) Graph the position, velocity, and acceleration functions for the first 7 s.
y
40
20
- 20
y
40
20
- 20
a
S
V
a
2
2
V
S
4
4
6
6
8
8
y
40
20
-20
y
40
20
-20
S
V
S
a
2
When, for 0 < t < ∞, is it slowing down? (Enter your answer in interval notation.)
2
a
(h) When, for 0 ≤ t < ∞, is the particle speeding up? (Enter your answer in interval notation.)
4
4
6
6
8
8
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage