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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)=³-12t² + 36t (a) Find the velocity at time t (in ft/s). v(t)-3²-24t+36 (b) What is the velocity (in ft/s) after 5 s? v(5) = -9 ✓ ft/s (c) When (in seconds) is the particle at rest? (smaller value) t = 2 ✓ S (larger value) t = 6 ✓ S (d) When (in seconds) is the particle moving in the positive direction? (Enter your answer using interval notation.) te [0,2) U (6,00) (e) Find the total distance (in feet) traveled during the first 7 s. ft (f) Find the acceleration at time t (in ft/s²). a(t) = 61-24 ✓ Find the acceleration (in ft/s2) after 5 s. a(5) = 6 ✓ ft/s² (9) Graph the position, velocity, and acceleration functions for the first 7 s. 40 20 -20 4 2 V 4 Junge 8 y 40 20 -20 V 4 2 4 (h) When, for 0 st<, is the particle speeding up? (Enter your answer using interval notation.) When, for 0 ≤ t < , is it slowing down? (Enter your answer using interval notation.) 6 E 8 $$ 4 6 8 40 20 -20 2 40 20 -20 V 2 6 Enge Q

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)=³-12t² + 36t (a) Find the velocity at time t (in ft/s). v(t)-3²-24t+36 (b) What is the velocity (in ft/s) after 5 s? v(5) = -9 ✓ ft/s (c) When (in seconds) is the particle at rest? (smaller value) t = 2 ✓ S (larger value) t = 6 ✓ S (d) When (in seconds) is the particle moving in the positive direction? (Enter your answer using interval notation.) te [0,2) U (6,00) (e) Find the total distance (in feet) traveled during the first 7 s. ft (f) Find the acceleration at time t (in ft/s²). a(t) = 61-24 ✓ Find the acceleration (in ft/s2) after 5 s. a(5) = 6 ✓ ft/s² (9) Graph the position, velocity, and acceleration functions for the first 7 s. 40 20 -20 4 2 V 4 Junge 8 y 40 20 -20 V 4 2 4 (h) When, for 0 st<, is the particle speeding up? (Enter your answer using interval notation.) When, for 0 ≤ t < , is it slowing down? (Enter your answer using interval notation.) 6 E 8 $$ 4 6 8 40 20 -20 2 40 20 -20 V 2 6 Enge Q

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
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...
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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 (in ft/s). v(t) = 31² 24t+36 (b) What is the velocity (in ft/s) after 5 s? v(5) = -9 I ft/s (c) When (in seconds) is the particle at rest? (smaller value) t = 2 ✔ S (larger value) t = 6 (d) When (in seconds) is the particle moving in the positive direction? (Enter your answer using interval notation.) te [0,2) U (6,00) (e) Find the total distance (in feet) traveled during the first 7 s. (f) Find the acceleration at time t (in ft/s²). a(t) = 6t 24 Find the acceleration (in ft/s2) after 5 s. a(5) = 6 ✓ ft/s² y (g) Graph the position, velocity, and acceleration functions for the first 7 s. 40 ft 20 S - 20 a 2 4 6 8 t y 40 20 A 2 a - 20 O (h) When, for 0 ≤ t < ∞, is the particle speeding up? (Enter your answer using interval notation.) When, for 0 < t < ∞, is it slowing down? (Enter your answer using interval notation.) 6 8 t DO y 40 20 -20 a 2 8 t y 40 20 -20 V 2 4 6 8 i
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 (in ft/s). v(t) = 31² 24t+36 (b) What is the velocity (in ft/s) after 5 s? v(5) = -9 I ft/s (c) When (in seconds) is the particle at rest? (smaller value) t = 2 ✔ S (larger value) t = 6 (d) When (in seconds) is the particle moving in the positive direction? (Enter your answer using interval notation.) te [0,2) U (6,00) (e) Find the total distance (in feet) traveled during the first 7 s. (f) Find the acceleration at time t (in ft/s²). a(t) = 6t 24 Find the acceleration (in ft/s2) after 5 s. a(5) = 6 ✓ ft/s² y (g) Graph the position, velocity, and acceleration functions for the first 7 s. 40 ft 20 S - 20 a 2 4 6 8 t y 40 20 A 2 a - 20 O (h) When, for 0 ≤ t < ∞, is the particle speeding up? (Enter your answer using interval notation.) When, for 0 < t < ∞, is it slowing down? (Enter your answer using interval notation.) 6 8 t DO y 40 20 -20 a 2 8 t y 40 20 -20 V 2 4 6 8 i
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