Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Use the result of Exercise 5.5.83 to compute the …

00:58

Question

Answered step-by-step

Problem 22 Medium Difficulty

If a freely falling body starts from rest, then its displacement is given by $ s = \frac{1}{2} gt^2 $. Let the velocity after a time $ T $ be $ v_T $. Show that if we compute the average of the velocities with respect to $ t $ we get $ v_{ave} = \frac{1}{2} v_T $, but if we compute the average of the velocities with respect to s we get $ v_{ave} = \frac{2}{3} v_T $.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Amrita Bhasin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Amrita Bhasin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Related Topics

Applications of Integration

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Join Course
Recommended Videos

14:18

If a freely falling body s…

01:05

If a freely falling body s…

01:52

The motion of a body falli…

07:48

For a freely falling objec…

03:56

Use the distance function …

02:39

Distance. For a freely fal…

Watch More Solved Questions in Chapter 6

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26

Video Transcript

recall the fact for this question that velocity is the derivative of position. In other words, ask prime of tea, as indicates position in this context. Therefore, the average lost you with respected teed one over tee times 1/2 This is 1/2 V of tea V s g t can t can be written this just simple algebraic manipulation as V over G. Therefore, V is the square root of two gs. Therefore we know that are average There's one over us Humanist es Juan the integral from us want us to the of STS is the same thing is one of her B minus A. And to grow from a bead on the function we're just using us Want us to in this context, therefore we end up with We're just putting in now what we know and then we have Diaz instead of GTX are variables s and this is a corpulent to 2/3 v of tea

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
162
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
70
Hosted by: Alonso M
See More

Related Topics

Applications of Integration

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

Recommended Videos

14:18

If a freely falling body starts from rest, then its displacement is given by $s…

01:05

If a freely falling body starts from rest, then its displacement is given by $s…

01:52

The motion of a body falling from rest in a resisting medium is described by th…

07:48

For a freely falling object starting from rest, $v_{0}=0$, find: (a) The averag…

03:56

Use the distance function $s(t)=16 t^{2}$ discussed on page 159 and in Example …

02:39

Distance. For a freely falling object, $a(t)=-32 \mathrm{ft} / \mathrm{sec}^{2}…
Additional Mathematics Questions

02:47

One card is selected at random from deck of cards. Determine the probability…

01:01

The critical F value with 6 numerator and 40 denominator degrees of freedom …

02:17

An urn contains 11 red balls and 9 white balls. Two balls are to be selected…

01:05

K(3) = Zand 93)=7, wnat is (( ^ 9XJR (+913) = (Bimplify your anster )

05:20

(4 pts ) A line passes through the point (0. and forims an angle of 0 = 5 w…

01:15

Sokie ta aquabon. 6 In Sx = 18
02
{} 0 B { {os} 0D 3/6}

01:03

Find four angles in different quadrants with the reference angle 30"_

05:15

Gloria would Iike to construct a bOx With volume of exactly 50ft3 using only…

10:06

Anatunal
butJuncd"
[UeLalt
Itom J] 7milon Mn 7uobio[7 e mlliun…

03:33

[-/3 Points]
DETAILS
For each of the following functions; determine th…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started