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when is the particle speeding up? When is the particle slowing down? Answer in interval notation.

when is the particle speeding up? When is the particle slowing down? Answer in interval notation.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Question
H) when is the particle speeding up? When is the particle slowing down? Answer in interval notation.
A graphing calculator is recommended. 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) = t - 9t2 + 24t (a) Find the velocity (in ft/s) at time t. v(t) = 31 - 18t + 24 ft/s (b) What is the velocity (in ft/s) after 1 second? v(1)I= 11 ft/s (c) When is the particle at rest? (Enter your answers as a comma-separated list.) t = 0 (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) -10 (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.
Transcribed Image Text:A graphing calculator is recommended. 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) = t - 9t2 + 24t (a) Find the velocity (in ft/s) at time t. v(t) = 31 - 18t + 24 ft/s (b) What is the velocity (in ft/s) after 1 second? v(1)I= 11 ft/s (c) When is the particle at rest? (Enter your answers as a comma-separated list.) t = 0 (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) -10 (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.
(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/s) at time t. a(t) = ft/s? Find the acceleration (in ft/s) after 1 second. a(1) = ft/s2 (g) Graph the position, velocity, and acceleration functions for 0 sts6. 30 30 20 20 10 10
Transcribed Image Text:(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/s) at time t. a(t) = ft/s? Find the acceleration (in ft/s) after 1 second. a(1) = ft/s2 (g) Graph the position, velocity, and acceleration functions for 0 sts6. 30 30 20 20 10 10
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