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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied.

Chapter 5.1, Problem 17E, The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car

To determine

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

Explanation

Given information:

The velocity with respect to time is a decreasing curve.

The curve lies in the interval between t=0 and t=6sec.

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 (Mn) is shown below:

Mn=v(t1)Δt+v(t2)Δt+...+v(tn)Δt (1)

Here, the mid height of the first rectangle is v(t1), the time interval is Δt,  the mid height of second rectangle is v(t2), and the mid height of nth rectangle is v(tn).

Take interval Δt as 1 sec and the number of rectangles as 6.

Draw six rectangles using mid endpoints for Δt=1 as shown below in Figure (1).

Refer Figure (1).

Take the mid height of the first rectangle’s v(t1) value as 55ft/sec, the mid height of second rectangle’s v(t2) value as 40ft/sec, the mid height of third rectangle’s v(t3) value as 28ft/sec, the mid height of fourth rectangle’s v(t4) value as 18ft/sec, the mid height of fifth rectangle’s v(t5) value as 10ft/sec, and the mid height of sixth rectangle’s v(t6) value as 4ft/sec

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