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) = 3t2-24t+36 (b) What is the velocity after 3 s? v(3) = ft/s (c) When is the particle at rest? t=s (smaller value) t=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) = 3t2-24t+36 (b) What is the velocity after 3 s? v(3) = ft/s (c) When is the particle at rest? t=s (smaller value) t=s (larger value)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![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)
3t2-24t+36
(b) What is the velocity after 3 s?
v(3) = 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
(0,2)U(6,00)
(e) Find the total distance traveled during the first 7 s.
ft
(f) Find the acceleration at time t.
a(t) =
=
6t-24
Find the acceleration after 3 s.
a(3) = ft/s²2
(g) Graph the position, velocity, and acceleration functions
for the first 7 s.
(h) When, for
0 ≤ t < 00,
is the particle speeding up? (Enter your answer in interval
notation.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F870ed321-0739-4fbf-a253-ce7df5f5de8f%2F28723f4e-356d-4cc3-9dde-0987e57ce0b7%2Fjz8g96_processed.jpeg&w=3840&q=75)
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)
3t2-24t+36
(b) What is the velocity after 3 s?
v(3) = 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
(0,2)U(6,00)
(e) Find the total distance traveled during the first 7 s.
ft
(f) Find the acceleration at time t.
a(t) =
=
6t-24
Find the acceleration after 3 s.
a(3) = ft/s²2
(g) Graph the position, velocity, and acceleration functions
for the first 7 s.
(h) When, for
0 ≤ t < 00,
is the particle speeding up? (Enter your answer in interval
notation.)
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