BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Solutions

Chapter
Section
BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem
1 views

The displacement (in feet) of a particle moving in a straight line is given by s = 1 2 t 2 6 t + 23 , where t is measured in seconds.

(a) Find the average velocity over each time interval:

(i) [4, 8]

(ii) [6, 8]

(iii) [8, 10]

(iv) [8, 12]

(b) Find the instantaneous velocity when. t = 8 .

(c) Draw the graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part (a). Then draw the tangent line whose slope is the instantaneous velocity in part (b).

To determine

a)To find::

The average velocity over time interval

Explanation

1) Formula:

The average velocity over a time interval [a,b] is given

Average velocity=sb-s(a)b-a

where s(t) is the displacement function.

2) Given:

s=12t2-6t+23.

3) Calculation:

i) The average velocity over time interval [4, 8]

Substitute the values of a = 4 and b = 8 in the average velocity formula, then

Average velocity=s8-s48-4

=1282-68+23-1242-64+234

=32-48+23-8+24-234

=04=0

ii) The average velocity over time interval [6, 8]

Substitute the values of a = 6 and b = 8 in the average velocity formula. Then we have

Average velocity=s8-s68-6

=1282-68+23-1262-66+232

=32-48+23-18+36-232

=22=1

iii) The average velocity over time interval [8, 10]

Substitute the values of a = 8 and b = 10 in the average velocity formula

To determine

(b)

To find::

The instantaneous velocity when t=8.

To determine

(c)

To plot:

The graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part (a). Then draw the tangent line whose slope is theinstantaneous velocity in part (b).

Explanation:

Calculus (MindTap Course List), Chapter 2.1, Problem 16E

The green curve is the displacement curve. The blue line is the tangent line whose slope in instantaneous velocity. The others are secant lines.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-2.1 P-11ESect-2.1 P-12ESect-2.1 P-13ESect-2.1 P-14ESect-2.1 P-15ESect-2.1 P-16ESect-2.1 P-17ESect-2.1 P-18ESect-2.1 P-19ESect-2.1 P-20ESect-2.1 P-21ESect-2.1 P-22ESect-2.1 P-23ESect-2.1 P-24ESect-2.1 P-25ESect-2.1 P-26ESect-2.1 P-27ESect-2.1 P-28ESect-2.1 P-29ESect-2.1 P-30ESect-2.1 P-31ESect-2.1 P-32ESect-2.1 P-33ESect-2.1 P-34ESect-2.1 P-35ESect-2.1 P-36ESect-2.1 P-37ESect-2.1 P-38ESect-2.1 P-39ESect-2.1 P-40ESect-2.1 P-41ESect-2.1 P-42ESect-2.1 P-43ESect-2.1 P-44ESect-2.1 P-45ESect-2.1 P-46ESect-2.1 P-47ESect-2.1 P-48ESect-2.1 P-49ESect-2.1 P-50ESect-2.1 P-51ESect-2.1 P-52ESect-2.1 P-53ESect-2.1 P-54ESect-2.1 P-55ESect-2.1 P-56ESect-2.1 P-57ESect-2.1 P-58ESect-2.1 P-59ESect-2.1 P-60ESect-2.1 P-61ESect-2.2 P-1ESect-2.2 P-2ESect-2.2 P-3ESect-2.2 P-4ESect-2.2 P-5ESect-2.2 P-6ESect-2.2 P-7ESect-2.2 P-8ESect-2.2 P-9ESect-2.2 P-10ESect-2.2 P-11ESect-2.2 P-12ESect-2.2 P-13ESect-2.2 P-14ESect-2.2 P-15ESect-2.2 P-16ESect-2.2 P-17ESect-2.2 P-18ESect-2.2 P-19ESect-2.2 P-20ESect-2.2 P-21ESect-2.2 P-22ESect-2.2 P-23ESect-2.2 P-24ESect-2.2 P-25ESect-2.2 P-26ESect-2.2 P-27ESect-2.2 P-28ESect-2.2 P-29ESect-2.2 P-30ESect-2.2 P-31ESect-2.2 P-32ESect-2.2 P-33ESect-2.2 P-34ESect-2.2 P-35ESect-2.2 P-36ESect-2.2 P-37ESect-2.2 P-38ESect-2.2 P-39ESect-2.2 P-40ESect-2.2 P-41ESect-2.2 P-42ESect-2.2 P-43ESect-2.2 P-44ESect-2.2 P-45ESect-2.2 P-46ESect-2.2 P-47ESect-2.2 P-48ESect-2.2 P-49ESect-2.2 P-50ESect-2.2 P-51ESect-2.2 P-52ESect-2.2 P-53ESect-2.2 P-54ESect-2.2 P-55ESect-2.2 P-56ESect-2.2 P-57ESect-2.2 P-58ESect-2.2 P-59ESect-2.2 P-60ESect-2.2 P-61ESect-2.2 P-62ESect-2.2 P-63ESect-2.2 P-64ESect-2.2 P-65ESect-2.3 P-1ESect-2.3 P-2ESect-2.3 P-3ESect-2.3 P-4ESect-2.3 P-5ESect-2.3 P-6ESect-2.3 P-7ESect-2.3 P-8ESect-2.3 P-9ESect-2.3 P-10ESect-2.3 P-11ESect-2.3 P-12ESect-2.3 P-13ESect-2.3 P-14ESect-2.3 P-15ESect-2.3 P-16ESect-2.3 P-17ESect-2.3 P-18ESect-2.3 P-19ESect-2.3 P-20ESect-2.3 P-21ESect-2.3 P-22ESect-2.3 P-23ESect-2.3 P-24ESect-2.3 P-25ESect-2.3 P-26ESect-2.3 P-27ESect-2.3 P-28ESect-2.3 P-29ESect-2.3 P-30ESect-2.3 P-31ESect-2.3 P-32ESect-2.3 P-33ESect-2.3 P-34ESect-2.3 P-35ESect-2.3 P-36ESect-2.3 P-37ESect-2.3 P-38ESect-2.3 P-39ESect-2.3 P-40ESect-2.3 P-41ESect-2.3 P-42ESect-2.3 P-43ESect-2.3 P-44ESect-2.3 P-45ESect-2.3 P-46ESect-2.3 P-47ESect-2.3 P-48ESect-2.3 P-49ESect-2.3 P-50ESect-2.3 P-51ESect-2.3 P-52ESect-2.3 P-53ESect-2.3 P-54ESect-2.3 P-55ESect-2.3 P-56ESect-2.3 P-57ESect-2.3 P-58ESect-2.3 P-59ESect-2.3 P-60ESect-2.3 P-61ESect-2.3 P-62ESect-2.3 P-63ESect-2.3 P-64ESect-2.3 P-65ESect-2.3 P-66ESect-2.3 P-67ESect-2.3 P-68ESect-2.3 P-69ESect-2.3 P-70ESect-2.3 P-71ESect-2.3 P-72ESect-2.3 P-73ESect-2.3 P-74ESect-2.3 P-75ESect-2.3 P-76ESect-2.3 P-77ESect-2.3 P-78ESect-2.3 P-79ESect-2.3 P-80ESect-2.3 P-81ESect-2.3 P-82ESect-2.3 P-83ESect-2.3 P-84ESect-2.3 P-85ESect-2.3 P-86ESect-2.3 P-87ESect-2.3 P-88ESect-2.3 P-89ESect-2.3 P-90ESect-2.3 P-91ESect-2.3 P-92ESect-2.3 P-93ESect-2.3 P-94ESect-2.3 P-95ESect-2.3 P-96ESect-2.3 P-97ESect-2.3 P-98ESect-2.3 P-99ESect-2.3 P-100ESect-2.3 P-101ESect-2.3 P-102ESect-2.3 P-103ESect-2.3 P-104ESect-2.3 P-105ESect-2.3 P-106ESect-2.3 P-107ESect-2.3 P-108ESect-2.3 P-109ESect-2.3 P-110ESect-2.4 P-1ESect-2.4 P-2ESect-2.4 P-3ESect-2.4 P-4ESect-2.4 P-5ESect-2.4 P-6ESect-2.4 P-7ESect-2.4 P-8ESect-2.4 P-9ESect-2.4 P-10ESect-2.4 P-11ESect-2.4 P-12ESect-2.4 P-13ESect-2.4 P-14ESect-2.4 P-15ESect-2.4 P-16ESect-2.4 P-17ESect-2.4 P-18ESect-2.4 P-19ESect-2.4 P-20ESect-2.4 P-21ESect-2.4 P-22ESect-2.4 P-23ESect-2.4 P-24ESect-2.4 P-25ESect-2.4 P-26ESect-2.4 P-27ESect-2.4 P-28ESect-2.4 P-29ESect-2.4 P-30ESect-2.4 P-31ESect-2.4 P-32ESect-2.4 P-33ESect-2.4 P-34ESect-2.4 P-35ESect-2.4 P-36ESect-2.4 P-37ESect-2.4 P-38ESect-2.4 P-39ESect-2.4 P-40ESect-2.4 P-41ESect-2.4 P-42ESect-2.4 P-43ESect-2.4 P-44ESect-2.4 P-45ESect-2.4 P-46ESect-2.4 P-47ESect-2.4 P-48ESect-2.4 P-49ESect-2.4 P-50ESect-2.4 P-51ESect-2.4 P-52ESect-2.4 P-53ESect-2.4 P-54ESect-2.4 P-55ESect-2.4 P-56ESect-2.4 P-57ESect-2.4 P-58ESect-2.5 P-1ESect-2.5 P-2ESect-2.5 P-3ESect-2.5 P-4ESect-2.5 P-5ESect-2.5 P-6ESect-2.5 P-7ESect-2.5 P-8ESect-2.5 P-9ESect-2.5 P-10ESect-2.5 P-11ESect-2.5 P-12ESect-2.5 P-13ESect-2.5 P-14ESect-2.5 P-15ESect-2.5 P-16ESect-2.5 P-17ESect-2.5 P-18ESect-2.5 P-19ESect-2.5 P-20ESect-2.5 P-21ESect-2.5 P-22ESect-2.5 P-23ESect-2.5 P-24ESect-2.5 P-25ESect-2.5 P-26ESect-2.5 P-27ESect-2.5 P-28ESect-2.5 P-29ESect-2.5 P-30ESect-2.5 P-31ESect-2.5 P-32ESect-2.5 P-33ESect-2.5 P-34ESect-2.5 P-35ESect-2.5 P-36ESect-2.5 P-37ESect-2.5 P-38ESect-2.5 P-39ESect-2.5 P-40ESect-2.5 P-41ESect-2.5 P-42ESect-2.5 P-43ESect-2.5 P-44ESect-2.5 P-45ESect-2.5 P-46ESect-2.5 P-47ESect-2.5 P-48ESect-2.5 P-49ESect-2.5 P-50ESect-2.5 P-51ESect-2.5 P-52ESect-2.5 P-53ESect-2.5 P-54ESect-2.5 P-55ESect-2.5 P-56ESect-2.5 P-57ESect-2.5 P-58ESect-2.5 P-59ESect-2.5 P-60ESect-2.5 P-61ESect-2.5 P-62ESect-2.5 P-63ESect-2.5 P-64ESect-2.5 P-65ESect-2.5 P-66ESect-2.5 P-67ESect-2.5 P-68ESect-2.5 P-69ESect-2.5 P-70ESect-2.5 P-71ESect-2.5 P-72ESect-2.5 P-73ESect-2.5 P-74ESect-2.5 P-75ESect-2.5 P-76ESect-2.5 P-77ESect-2.5 P-78ESect-2.5 P-79ESect-2.5 P-80ESect-2.5 P-81ESect-2.5 P-82ESect-2.5 P-83ESect-2.5 P-84ESect-2.5 P-85ESect-2.5 P-86ESect-2.5 P-87ESect-2.5 P-88ESect-2.5 P-89ESect-2.5 P-90ESect-2.6 P-1ESect-2.6 P-2ESect-2.6 P-3ESect-2.6 P-4ESect-2.6 P-5ESect-2.6 P-6ESect-2.6 P-7ESect-2.6 P-8ESect-2.6 P-9ESect-2.6 P-10ESect-2.6 P-11ESect-2.6 P-12ESect-2.6 P-13ESect-2.6 P-14ESect-2.6 P-15ESect-2.6 P-16ESect-2.6 P-17ESect-2.6 P-18ESect-2.6 P-19ESect-2.6 P-20ESect-2.6 P-21ESect-2.6 P-22ESect-2.6 P-23ESect-2.6 P-24ESect-2.6 P-25ESect-2.6 P-26ESect-2.6 P-27ESect-2.6 P-28ESect-2.6 P-29ESect-2.6 P-30ESect-2.6 P-31ESect-2.6 P-32ESect-2.6 P-33ESect-2.6 P-34ESect-2.6 P-35ESect-2.6 P-36ESect-2.6 P-37ESect-2.6 P-38ESect-2.6 P-39ESect-2.6 P-40ESect-2.6 P-41ESect-2.6 P-42ESect-2.6 P-43ESect-2.6 P-44ESect-2.6 P-45ESect-2.6 P-46ESect-2.6 P-47ESect-2.6 P-48ESect-2.6 P-49ESect-2.6 P-50ESect-2.6 P-51ESect-2.6 P-52ESect-2.6 P-53ESect-2.6 P-54ESect-2.6 P-55ESect-2.6 P-56ESect-2.6 P-57ESect-2.6 P-58ESect-2.6 P-59ESect-2.6 P-60ESect-2.6 P-61ESect-2.6 P-62ESect-2.7 P-1ESect-2.7 P-2ESect-2.7 P-3ESect-2.7 P-4ESect-2.7 P-5ESect-2.7 P-6ESect-2.7 P-7ESect-2.7 P-8ESect-2.7 P-9ESect-2.7 P-10ESect-2.7 P-11ESect-2.7 P-12ESect-2.7 P-13ESect-2.7 P-14ESect-2.7 P-15ESect-2.7 P-16ESect-2.7 P-17ESect-2.7 P-18ESect-2.7 P-19ESect-2.7 P-20ESect-2.7 P-21ESect-2.7 P-22ESect-2.7 P-23ESect-2.7 P-24ESect-2.7 P-25ESect-2.7 P-26ESect-2.7 P-27ESect-2.7 P-28ESect-2.7 P-29ESect-2.7 P-30ESect-2.7 P-31ESect-2.7 P-32ESect-2.7 P-33ESect-2.7 P-34ESect-2.7 P-35ESect-2.7 P-36ESect-2.8 P-1ESect-2.8 P-2ESect-2.8 P-3ESect-2.8 P-4ESect-2.8 P-5ESect-2.8 P-6ESect-2.8 P-7ESect-2.8 P-8ESect-2.8 P-9ESect-2.8 P-10ESect-2.8 P-11ESect-2.8 P-12ESect-2.8 P-13ESect-2.8 P-14ESect-2.8 P-15ESect-2.8 P-16ESect-2.8 P-17ESect-2.8 P-18ESect-2.8 P-19ESect-2.8 P-20ESect-2.8 P-21ESect-2.8 P-22ESect-2.8 P-23ESect-2.8 P-24ESect-2.8 P-25ESect-2.8 P-26ESect-2.8 P-27ESect-2.8 P-28ESect-2.8 P-29ESect-2.8 P-30ESect-2.8 P-31ESect-2.8 P-32ESect-2.8 P-33ESect-2.8 P-34ESect-2.8 P-35ESect-2.8 P-36ESect-2.8 P-37ESect-2.8 P-38ESect-2.8 P-39ESect-2.8 P-40ESect-2.8 P-41ESect-2.8 P-42ESect-2.8 P-43ESect-2.8 P-44ESect-2.8 P-45ESect-2.8 P-46ESect-2.8 P-47ESect-2.8 P-48ESect-2.8 P-49ESect-2.8 P-50ESect-2.9 P-1ESect-2.9 P-2ESect-2.9 P-3ESect-2.9 P-4ESect-2.9 P-5ESect-2.9 P-6ESect-2.9 P-7ESect-2.9 P-8ESect-2.9 P-9ESect-2.9 P-10ESect-2.9 P-11ESect-2.9 P-12ESect-2.9 P-13ESect-2.9 P-14ESect-2.9 P-15ESect-2.9 P-16ESect-2.9 P-17ESect-2.9 P-18ESect-2.9 P-19ESect-2.9 P-20ESect-2.9 P-21ESect-2.9 P-22ESect-2.9 P-23ESect-2.9 P-24ESect-2.9 P-25ESect-2.9 P-26ESect-2.9 P-27ESect-2.9 P-28ESect-2.9 P-29ESect-2.9 P-30ESect-2.9 P-31ESect-2.9 P-32ESect-2.9 P-33ESect-2.9 P-34ESect-2.9 P-35ESect-2.9 P-36ESect-2.9 P-37ESect-2.9 P-38ESect-2.9 P-39ESect-2.9 P-40ESect-2.9 P-41ESect-2.9 P-42ESect-2.R P-1CCSect-2.R P-2CCSect-2.R P-3CCSect-2.R P-4CCSect-2.R P-5CCSect-2.R P-6CCSect-2.R P-7CCSect-2.R P-8CCSect-2.R P-9CCSect-2.R P-10CCSect-2.R P-11CCSect-2.R P-12CCSect-2.R P-1TFQSect-2.R P-2TFQSect-2.R P-3TFQSect-2.R P-4TFQSect-2.R P-5TFQSect-2.R P-6TFQSect-2.R P-7TFQSect-2.R P-8TFQSect-2.R P-9TFQSect-2.R P-10TFQSect-2.R P-11TFQSect-2.R P-12TFQSect-2.R P-13TFQSect-2.R P-14TFQSect-2.R P-15TFQSect-2.R P-1ESect-2.R P-2ESect-2.R P-3ESect-2.R P-4ESect-2.R P-5ESect-2.R P-6ESect-2.R P-7ESect-2.R P-8ESect-2.R P-9ESect-2.R P-10ESect-2.R P-11ESect-2.R P-12ESect-2.R P-13ESect-2.R P-14ESect-2.R P-15ESect-2.R P-16ESect-2.R P-17ESect-2.R P-18ESect-2.R P-19ESect-2.R P-20ESect-2.R P-21ESect-2.R P-22ESect-2.R P-23ESect-2.R P-24ESect-2.R P-25ESect-2.R P-26ESect-2.R P-27ESect-2.R P-28ESect-2.R P-29ESect-2.R P-30ESect-2.R P-31ESect-2.R P-32ESect-2.R P-33ESect-2.R P-34ESect-2.R P-35ESect-2.R P-36ESect-2.R P-37ESect-2.R P-38ESect-2.R P-39ESect-2.R P-40ESect-2.R P-41ESect-2.R P-42ESect-2.R P-43ESect-2.R P-44ESect-2.R P-45ESect-2.R P-46ESect-2.R P-47ESect-2.R P-48ESect-2.R P-49ESect-2.R P-50ESect-2.R P-51ESect-2.R P-52ESect-2.R P-53ESect-2.R P-54ESect-2.R P-55ESect-2.R P-56ESect-2.R P-57ESect-2.R P-58ESect-2.R P-59ESect-2.R P-60ESect-2.R P-61ESect-2.R P-62ESect-2.R P-63ESect-2.R P-64ESect-2.R P-65ESect-2.R P-66ESect-2.R P-67ESect-2.R P-68ESect-2.R P-69ESect-2.R P-70ESect-2.R P-71ESect-2.R P-72ESect-2.R P-73ESect-2.R P-74ESect-2.R P-75ESect-2.R P-76ESect-2.R P-77ESect-2.R P-78ESect-2.R P-79ESect-2.R P-80ESect-2.R P-81ESect-2.R P-82ESect-2.R P-83ESect-2.R P-84ESect-2.R P-85ESect-2.R P-86ESect-2.R P-87ESect-2.R P-88ESect-2.R P-89ESect-2.R P-90ESect-2.R P-91ESect-2.R P-92ESect-2.P P-1PSect-2.P P-2PSect-2.P P-3PSect-2.P P-4PSect-2.P P-5PSect-2.P P-6PSect-2.P P-7PSect-2.P P-8PSect-2.P P-9PSect-2.P P-10PSect-2.P P-11PSect-2.P P-12PSect-2.P P-13PSect-2.P P-14PSect-2.P P-15PSect-2.P P-16PSect-2.P P-17PSect-2.P P-18PSect-2.P P-19PSect-2.P P-20PSect-2.P P-21PSect-2.P P-22PSect-2.P P-23PSect-2.P P-24PSect-2.P P-25PSect-2.P P-26PSect-2.P P-27PSect-2.P P-28P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Other Equations Find all real solutions of the equation. 114. |2x| = 3

Precalculus: Mathematics for Calculus (Standalone Book)

Fill in the blanks. 7. If limxaf(x) = L and limxag(x) = M, then a. limxa[f(x)]r, where r is a positive constant...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In Problems 25-34, use the matrices below. Perform the indicated operations.

Mathematical Applications for the Management, Life, and Social Sciences

Find the derivative of the function. y = esin 2x + sin(e2x)

Single Variable Calculus: Early Transcendentals

True or False: (x + y)y″ + (x − 10)y′ + xy + 10 = 0 is homogeneous.

Study Guide for Stewart's Multivariable Calculus, 8th

The harmonic series is: 1 + 2 + 3 + 4 + …

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th