A particle moves according to a law of motions = 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-24Find the acceleration after 3 s.a(3) = ft/s²2(g) Graph the position, velocity, and acceleration functionsfor the first 7 s.(h) When, for0 ≤ t < 00,is the particle speeding up? (Enter your answer in intervalnotation.)

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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)

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

Section: Chapter Questions

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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Distance and Speed

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Question

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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