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

The speed, distance and time relation forms the basis of study of motion. You will need these concepts in the study of Mechanics. This concept is applicable for students who are studying the following courses –

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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