   Chapter 11.11, Problem 31E

Chapter
Section
Textbook Problem

A car is moving with speed 20 m/s and acceleration 2  m/s 2 at a given instant. Using a second-degree Taylor polynomial, estimate how far the car moves in the next second. Would it be reasonable to use this polynomial to estimate the distance traveled during the next minute?

To determine

To estimate:

How far does the car move in the next second?

Explanation

1) Concept:

velocity=rate of change of position with time

acceleration=rate of change of velocity with  time

2) Calculation:

Let s(t) be the position function of the car,  v(t) be the velocity of car and a(t) be the acceleration of the car

Suppose, initially, the car is at position 0

That is s0=0

It is given that  Velocity, vt=20m/s and acceleration, at=2m/s2

Velocity, vt=s'(t) and acceleration,at=s''(t)

Therefore,  second degree polynomial T2(t)  at 0 for position function s(t) is,

T2

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 