Suppose the position of an object moving horizontally after t seconds is given by the following function s=f(t), where s is measured in feet, with s>0 corresponding to p origin. a. Graph the position function. b. Find and graph the velocity function. When is the object stationary, moving to the right, and moving to the left? c. Determine the velocity and acceleration of the object at t=1. d. Determine the acceleration of the object when its velocity is zero. e. On what intervals is the speed increasing? f(t)=t3-9t2 +24t; 0 st≤6 When is the object stationary? t= (Simplify your answer. Use a comma to separate answers as needed.) When is the object moving to the right? The object is moving to the right on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) When is the object moving to the left? The object is moving to the left on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) c. The velocity of the object at t = 1 is The acceleration of the object at t = 1 is (Simplify your answer.) (Simplify your answer.) d. The acceleration each time the velocity is zero is (Simplify your answer. Use a comma to separate answers as needed.) e. On what intervals is the speed increasing?
Suppose the position of an object moving horizontally after t seconds is given by the following function s=f(t), where s is measured in feet, with s>0 corresponding to p origin. a. Graph the position function. b. Find and graph the velocity function. When is the object stationary, moving to the right, and moving to the left? c. Determine the velocity and acceleration of the object at t=1. d. Determine the acceleration of the object when its velocity is zero. e. On what intervals is the speed increasing? f(t)=t3-9t2 +24t; 0 st≤6 When is the object stationary? t= (Simplify your answer. Use a comma to separate answers as needed.) When is the object moving to the right? The object is moving to the right on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) When is the object moving to the left? The object is moving to the left on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) c. The velocity of the object at t = 1 is The acceleration of the object at t = 1 is (Simplify your answer.) (Simplify your answer.) d. The acceleration each time the velocity is zero is (Simplify your answer. Use a comma to separate answers as needed.) e. On what intervals is the speed increasing?
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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Transcribed Image Text:Suppose the position of an object moving horizontally after t seconds is given by the following function s=f(t), where s is measured in feet, with s>0 corresponding to p
origin.
a. Graph the position function.
b. Find and graph the velocity function. When is the object stationary, moving to the right, and moving to the left?
c. Determine the velocity and acceleration of the object at t=1.
d. Determine the acceleration of the object when its velocity is zero.
e. On what intervals is the speed increasing?
f(t)=t3-9t2 +24t; 0 st≤6
When is the object stationary?
t=
(Simplify your answer. Use a comma to separate answers as needed.)
When is the object moving to the right?
The object is moving to the right on the interval(s)
(Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)
When is the object moving to the left?
The object is moving to the left on the interval(s)
(Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)
c. The velocity of the object at t = 1 is
The acceleration of the object at t = 1 is
(Simplify your answer.)
(Simplify your answer.)
d. The acceleration each time the velocity is zero is
(Simplify your answer. Use a comma to separate answers as needed.)
e. On what intervals is the speed increasing?
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