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A particle moves according to a law of motion s= f(t), tz 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t)=3-9² +24t (a) Find the velocity (in ft/s) at time t. v(t)= ft/s (b) What is the velocity (in ft/s) after 1 second? v(1) = (c) When is the particle at rest? (Enter your answers as a comma-separated list.) (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds. ft (f) Find the acceleration (in ft/s2) at time t. a(t) = ft/s² Find the acceleration (in ft/s2) after 1 second. a(1) - ft/s² (9) Graph the position, velocity, and acceleration functions for 0 st s 6. 30 ft/s 20 10 -10 8 a 1 2 5 6 30 When is it slowing down? (Enter your answer using interval notation.) 20 10 -10 (h) When is the particle speeding up? (Enter your answer using interval notation.) a 1 5 6 t 30 @O 20 10 -10 P a 1 5 J 1 4 5 30 20 10 -10 P a 6 t C

A particle moves according to a law of motion s= f(t), tz 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t)=3-9² +24t (a) Find the velocity (in ft/s) at time t. v(t)= ft/s (b) What is the velocity (in ft/s) after 1 second? v(1) = (c) When is the particle at rest? (Enter your answers as a comma-separated list.) (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds. ft (f) Find the acceleration (in ft/s2) at time t. a(t) = ft/s² Find the acceleration (in ft/s2) after 1 second. a(1) - ft/s² (9) Graph the position, velocity, and acceleration functions for 0 st s 6. 30 ft/s 20 10 -10 8 a 1 2 5 6 30 When is it slowing down? (Enter your answer using interval notation.) 20 10 -10 (h) When is the particle speeding up? (Enter your answer using interval notation.) a 1 5 6 t 30 @O 20 10 -10 P a 1 5 J 1 4 5 30 20 10 -10 P a 6 t C

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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. (If an answer does not exist, enter DNE.) f(t) = t³ 9t² + 24t (a) Find the velocity (in ft/s) at time t. v(t) = (b) What is the velocity (in ft/s) after 1 second? v(1) = t = (c) When is the particle at rest? (Enter your answers as a comma-separated list.) (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds. ft a(t) = (f) Find the acceleration (in ft/s2) at time t. ft/s² a(1) = ft/s Find the acceleration (in ft/s²) after 1 second. ft/s² ft/s (g) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 6. 30 20 a 1 2 4 5 10 -10 S a 6 t 30 When is it slowing down? (Enter your answer using interval notation.) 20 10 -10 (h) When is the particle speeding up? (Enter your answer using interval notation.) S a 1 4 5 6 30 20 10 -10 a 1 2 4 5 6 A 1 2 4 5 30 20 10 - 10 a 6
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. (If an answer does not exist, enter DNE.) f(t) = t³ 9t² + 24t (a) Find the velocity (in ft/s) at time t. v(t) = (b) What is the velocity (in ft/s) after 1 second? v(1) = t = (c) When is the particle at rest? (Enter your answers as a comma-separated list.) (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds. ft a(t) = (f) Find the acceleration (in ft/s2) at time t. ft/s² a(1) = ft/s Find the acceleration (in ft/s²) after 1 second. ft/s² ft/s (g) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 6. 30 20 a 1 2 4 5 10 -10 S a 6 t 30 When is it slowing down? (Enter your answer using interval notation.) 20 10 -10 (h) When is the particle speeding up? (Enter your answer using interval notation.) S a 1 4 5 6 30 20 10 -10 a 1 2 4 5 6 A 1 2 4 5 30 20 10 - 10 a 6
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