Chapter 5.5, Problem 16E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

The velocity graph of an accelerating car is shown.

(a) Use the Midpoint Rule to estimate the average velocity of the car during the first 12 seconds.

(b) what time was the instantaneous velocity equal to the average velocity?

To determine

**(a)**

**To estimate:**

The average velocity of a car during the first

Explanation

**1) Concept:**

Use the mean value theorem for integrals and the midpoint rule to estimate the average velocity of the car.

**2) Mean Value Theorem for IntegralsandMidpoint rule:**

The Mean Value Theorem: If

that is,

The midpoint rule:

where

**3) Calculation:**

By using the mean value theorem for integrals:

Here,

The average velocity of the car during the first

Since we can change the variable in the integration,

Use themidpoint rule.

With

Substitute values.

The three subintervals are

To determine

**(b)**

**To find:**

The time where the instantaneous velocity equal to the average velocity

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