   Chapter 11.11, Problem 31E

Chapter
Section
Textbook Problem

# A car is moving with speed 20 m/s and acceleration 2 m/s2 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: The distance that the car moves in the next second using a second-degree Taylor polynomial and find whether this method is reasonable to estimate the distance travelled during the next minute.

Explanation

The initial velocity of the car is 20m/s.

The acceleration of the car is 2m/s.

Let s(t) be the position vector.

Then,

s(t)=12at2+vt+s0=122t2+20t+0[s0 is the initial point]=t2+20t

The position, velocity and acceleration is as follows.

s(t)=t2+20tv(t)=2t+20a(t)=2

Then, the second degree Taylor polynomial is,

T2=s(0

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