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) = 31² - 24t+36 (b) What is the velocity after 5 s? v(5) = -9 ft/s (c) When is the particle at rest? 2 t = 6 s (smaller value) s (larger value) (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)=

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) = 31² - 24t+36 (b) What is the velocity after 5 s? v(5) = -9 ft/s (c) When is the particle at rest? 2 t = 6 s (smaller value) s (larger value) (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)=

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 45SE: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the...

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Question

I need help answering parts D, E, and F. The first 3 parts are already solved. Thank you!

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) = 31² 24t+36
(b) What is the velocity after 5 s?
v(5) = -9
ft/s
(c) When is the particle at rest?
t = 2
t = 6
s (smaller value)
s (larger value)
(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) =

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