Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.4, Problem 39E

To determine

To find the cart’s maximum speed.

Expert Solution

Answer to Problem 39E

The Maximum speed of 10π at t=12,32,52and72 , position of 0 cm ,acceleration of 0cm/sec2

Explanation of Solution

Given maximum speed.

Calculation:

Find s′ using chain rule to find the velocity function.

v=s′=−2sinπt⋅π =−10πsinπta=v′=−10πcosπt⋅π =−10π2cosπtset v′equal to 0 and solve for t−10πcosπt=0cosπt=0πt=π2+πkt=12+k

k=0→t=12:v=−10πsin(π⋅12)=−10πk=1→t=32:v=−10πsin(π⋅32)=10πk=2→t=52:v=−10πsin(π⋅52)=−10πk=3→t=72:v=−10πsin(π⋅72)=10π

t=12:s=10cosπ2=0t=32:s=10cos3π2=0t=52:s=10cos5π2=0t=72:s=10cos7π2=0t=12:a=−10π2cosπ2=0t=32:a=−10π2cosπ2=0t=52:a=−10π2cosπ2=0t=72:a=−10π2cosπ2=0

Thus, the Maximum speed of 10π at t=12,32,52and72 , position of 0 cm ,acceleration of 0cm/sec2 .

To determine

To find the cart’s maximum speed.

Expert Solution

Answer to Problem 39E

The cart‘s speed is 10cm or−10cm,0 cm/sec .

Explanation of Solution

Given maximum speed.

Calculation:

Find s′ using chain rule to find the velocity function.

s=10cosπts′=10(−sinπt)(π) =−10πsinπts′′=−10π(cosπt)(π) =−10π2cosπtsince−1≤cosπt≤1 for all t cosπt=±1 πt=0,π,2π,3π.... t=0,1,2,3..... s=10cosπts(0)=10cos(π⋅0) =10cos0 =10s(1)=10cos(π⋅1) =10cosπ =−10s′=−10πsinπt s′(0)=−10πsin(π⋅0) =−10πsin0 =0s′(1)=−10πsin(π⋅1) =−10πsinπ =−10(0) =0

Thus, the cart‘s speed is 10cm or−10cm,0 cm/sec .

Chapter 5.4, Problem 38E

Chapter 5.4, Problem 40E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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