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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 5.1, Problem 15E

To determine

The distance traveled by the car when the brakes are applied.

Expert Solution

The distance traveled by the car is 155 ft.

**Given information:**

The velocity with respect to time is a decreasing curve.

The curve lies in the interval between

Use right endpoints as a lower estimate, left end points as an upper estimate, and mid endpoints as mid estimate due to a decreasing velocity curve with respect to time.

The expression to find the distance using mid estimate

Here, the mid height of the first rectangle is *n*^{th} rectangle is

Take interval

Draw six rectangles using mid endpoints for

Refer Figure (1).

Take the mid height of the first rectangle’s

Substitute 6 for *n*, 55ft/sec for

Therefore, the mid estimate using mid endpoints for

Check whether the estimated value is reasonable or not:

Find the area of triangle (*A*) as shown below:

Here, the width of triangle is *b* and the height of the triangle is *h*.

Refer to Figure (1).

Assume the curve as a triangle by drawing a line from

Take the width of triangle *b* value as 6 sec and the height of the triangle *h* value as 70 ft/sec.

Substitute 6 sec for *b* and 70 ft/sec for *h* in Equation (2).

The assumed triangle value is an overestimate compared to the calculated mid estimate value as 155 ft.

So the calculated mid estimate is a reasonable value.

Hence, the distance travelled by the car is 155 ft when the brakes are applied.