Download the App!

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

Sent to:
  • Textbooks
  • Test Prep
  • Numerade for Schools
  • Bootcamps
  • Class
  • Ask Question
  • StudyParty
  • Earn Money
    Refer a friend. Get $50! Become an Educator
  • Log in

Problem

(II) A world-class sprinter can reach a top speed…

01:50
preview
Numerade Logo

Get the answer to your homework problem.

Try Numerade free for 7 days

Josh B.
Numerade Educator

Like

Report

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 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 89 Problem 90 Problem 91 Problem 92 Problem 93 Problem 94 Problem 95 Problem 96 Problem 97

Problem 34 Hard Difficulty

(II) Show that $\overline{v}=\left(v+v_{0}\right) / 2$ (see Eq. 12 $\mathrm{d} )$ is not valid when the acceleration $a=A+B t,$ where $A$ and $B$ are constants.

Answer

$\bar{v} \neq \frac{1}{2}\left(v+v_{0}\right)$

Related Courses

Physics 101 Mechanics

Physics for Scientists and Engineers with Modern Physics

Chapter 2

Describing Motion: Kinematics in One Dimension

Related Topics

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Discussion

You must be signed in to discuss.
Top Physics 101 Mechanics Educators
Elyse G.

Cornell University

Farnaz M.

Simon Fraser University

Jared E.

University of Winnipeg

Meghan M.

McMaster University

Physics 101 Mechanics Courses

Lectures

Video Thumbnail

03:28

Newton's Laws - Intro

Newton's Laws of Moti…

Video Thumbnail

04:16

Math Review - Intro

In mathematics, a proof is…

Join Course
Recommended Videos

01:08

Show that for motion in a …

00:41

Show that for motion in a …

03:35

CE Which of the following …

01:55

Relationship between $\mat…

03:09

Suppose that object A is l…

02:10

The acceleration of a part…

04:38

(III) Show that the equati…

02:52

Show that if acceleration …

02:50

(II) The position of an ob…

00:21

Fill in the blanks.

…

09:17

If the acceleration a is c…

03:02

(III) The acceleration of …

00:33

A particle's position…

03:11

What if the acceleration i…

01:59

The equation of motion of …

09:09

$$\begin{array}{c}{\text {…

01:42

Give the acceleration $a=d…

07:07

Motion Along a Line positi…

03:35

CE Which of the following …

06:24

An object starts moving in…

Watch More Solved Questions in Chapter 2

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
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86
Problem 87
Problem 88
Problem 89
Problem 90
Problem 91
Problem 92
Problem 93
Problem 94
Problem 95
Problem 96
Problem 97

Video Transcript

This is quite an interesting problem. It's very theoretical. So we want to show that this equation for the average velocity where's some of being V zero over to? We want to show that this is not valid when we have an acceleration of this form A plus b t where a and B are constants. So this this acceleration is represents exploration. That's not constant. And to show that the this average velocity equation doesn't work here, we're gonna need a little bit calculus. So I know that I can say aye is d X, not X TV, B t. And then we can say from that that are Devi is a d t pretty simple. And now we need to integrate. So I'm gonna integrate Devi and A T. T and the bounds of this inter girl. I want to go from V zero our initial velocity to V and I'm going to go from a time of 02 time t And from here we just get V going from V zero to V and on the right side, we want the integral from zero to t in. Our acceleration is a plus. B t DT. So the left side just comes out to V minus Be zero on the right side comes out to a T plus 1/2 B t squared And now I can find an expression for the velocity Gonna be v zero plus 80 plus 1/2 feet Peachy is great And now do the same thing that I just did, but with velocity. So I know that velocity is dx DT. And so I can say that d x is VD p andl integrate once again and the bounce of my integral I'm going to go from a position x zero to x and again from time zero to time t So just like the last in the grill, we're going to get X minus x zero and our velocity function. It's what we solved The last part be zero plus 80 plus 1/2 beachy squared. So this integral comes out to be, uh, let's see, B zero The first term we had a T second term is gonna be 1/2 a T squared this term t squared Integral is gonna be 1/3 t cubed and 1/3 time's 1/2 is 1/6 b t cute and so I can get an expression for a position is x zero plus B zero t that this should be a plus plus 1/2 a T squared plus 1/6 beachy cute. And now I'm gonna go back to this. What we're trying to show, uh doesn't work. So I have V equals our average V is V plus B zero over, too. And to make things easier, so we have this function for position and this function for velocity. I'm just going to set, uh, V zero and zero 20 Because why not? It doesn't make a difference. And so then we're gonna get for our average velocity. I'm going to get V over, too. Just gonna be a t plus 1/2 p d squared over two. We get 1/2 80 plus one over four b t squared. So that's what we get if we use this equation for average velocity and then we want to show that that doesn't work. So we know that average velocity is always going to be Delta X over Delta T. This is always true. And so if we plug in Delta X here Ah, actually, we don't even need X zero to be zero because we have Delta X. It doesn't matter, but we still know v 00 So this is gonna be 1/2 80 squared plus 1/6 b t cubed over our delta Tea is just tea because you're going from zero to T. And so this is 1/2 a T plus 1/6 B t squared. And now you can see we have this value for first equation just not equal to what we get when we used all the ex of adult teeth. So that says that when our acceleration isn't of the form A plus B t which is not constant than this equation here, V equals half of V plus B zero does not work.

Get More Help with this Textbook
Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics

View More Answers From This Book

Find Another Textbook

Related Topics

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Top Physics 101 Mechanics Educators
Elyse G.

Cornell University

Farnaz M.

Simon Fraser University

Jared E.

University of Winnipeg

Meghan M.

McMaster University

Physics 101 Mechanics Courses

Lectures

Video Thumbnail

03:28

Newton's Laws - Intro

Newton's Laws of Motion are three physical laws that, laid the foundati…

Video Thumbnail

04:16

Math Review - Intro

In mathematics, a proof is a sequence of statements given to explain how a c…

Join Course
Recommended Videos

01:08

Show that for motion in a straight line with constant acceleration $ a $, initi…

00:41

Show that for motion in a straight line with constant acceleration $a$ , initia…

03:35

CE Which of the following equations are dimensionally consistent? (a) $v=a t,$ …

01:55

Relationship between $\mathrm{T}, \mathrm{N},$ and a Show that if an object acc…

03:09

Suppose that object A is located at $s=0$ at time $t=0$ and starts moving along…

02:10

The acceleration of a particle is defined by the relation $a=k t^{2}$. (a) Know…

04:38

(III) Show that the equation for the stopping distance of a car is $d_{\mathrm{…

02:52

Show that if acceleration is constant, then the change in velocity is proporti…

02:50

(II) The position of an object is given by $x=A t+B t^{2}$ , where $x$ is in m…

00:21

Fill in the blanks. The equation $ s = \dfrac{1}{2} at^2 + v_0t + s_0 $ …

09:17

If the acceleration a is constant, show that $\mathbf{L}^{-\infty}=\mathbf{0}.$

03:02

(III) The acceleration of an object (in $\mathrm{m} / \mathrm{s}^{2} )$ is meas…

00:33

A particle's position is given by $s=t^{3}-6 t^{2}+9 t .$ What is its accelerat…

03:11

What if the acceleration is not constant? A particle starts from the origin wit…

01:59

The equation of motion of a particle is $ = t^3 - 3t, $ where is in meters and …

09:09

$$\begin{array}{c}{\text { Motion Under Gravity Show that an object thrown from…

01:42

Give the acceleration $a=d^{2} s / d t^{2},$ initial velocity, and initial posi…

07:07

Motion Along a Line position $s=f(t)$ of an object moving up and down on a coor…

03:35

CE Which of the following equations are dimensionally consistent? (a) $x=\frac{…

06:24

An object starts moving in a straight line from position $x_{0}$, at time $t=0,…
Additional Physics Questions
ii-on-an-audio-compact-disc-cd-digital-bits-of-information-are-encoded-sequentially-along-a-spi

02:39

(II) On an audio compact disc (CD), digital bits of information are encoded …

bullet-when-a-toy-car-is-rapidly-scooted-across-the-floor-it-stores-energy-in-a-flywheel-the-c

03:11

$\bullet$ When a toy car is rapidly scooted across the floor, it stores
e…

bulletbullet-surface-tension-surface-tension-is-the-force-that-causes-the-surface-of-water

01:39

$\bullet$$\bullet$ Surface tension. Surface tension is the force that causes…

a-deuteron-particle-the-nucleus-of-an-isotope-of-hydrogen-consisting-of-one-proton-and-one-neutron

02:10

A deuteron particle (the nucleus of an isotope of hydrogen consisting of one…

beginarrayltext-the-density-of-an-object-is-defined-as-its-mass-divided-by-its-t

02:17

$$ \begin{array}{l}{\text { The density of an object is defined as its mass …

in-redesigning-a-piece-of-equipment-you-need-to-replace-a-solid-spherical-part-of-mass-m-with-a-h

01:46

In redesigning a piece of equipment, you need to replace a solid spherical p…

bullet-the-pulley-in-fig-937-has-radius-r-and-a-moment-of-inertia-i-the-rope-does-not-sli

03:10

$\bullet$ The pulley in Fig. 9.37 has radius $R$ and a moment of inertia $I$…

bullet-bullet-a-an-electron-is-moving-east-in-a-uniform-electric-field-of-150-mathrmn

03:55

$\bullet$ $\bullet$ (a) An electron is moving east in a uniform electric fie…

1-a-delivery-truck-travels-28-blocks-north-16-blocks-east-and-26-blocks-south-what-is-its-final

05:25

(1) A delivery truck travels 28 blocks north, 16 blocks east, and 26 blocks …

bullet-bullet-torque-and-force-on-a-dipole-an-electric-dipole-is-in-a-uniform-external-elec

05:28

$\bullet$ $\bullet$ Torque and force on a
dipole. An electric dipole is i…

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
  • Topics
  • Test Prep
  • Ask Directory
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started