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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

The table shows speedometer readings at 10-second intervals during a 1-minute period for a car racing at the Daytona International Speedway in Florida.

(a) Estimate the distance the race car traveled during this

Time (s) Velocity (mi/h)
0 182.9
10 168.0
20 106.6
30 99.8
40 124.5
50 176.1
60 175.6

time period using the velocities at the beginning of the time intervals.

(b) Give another estimate using the velocities at the end of the time periods.

(c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.

To determine

a)

To estimate:

The distance the race car traveled during the given period

Explanation

1) Concept:

i. Use the formula

Distance = time * velocity

ii. Convert miles per hour into feet per second.

1 mi/h=52803600 ft/s

2) Calculation:

To estimate the distance the race car traveled during 1- minute time period using the velocities at the beginning of the time intervals.

First convert the given velocity into feet per second

Then find distance traveled during each interval.

For interval 0 to 10,

Distance =182.9×52803600268.25

For interval 10 to 20,

Distance =168×52803600=246.4

For interval 20 to 30,

Distance =106.6×52803600156.36

For interval 30 to 40,

Distance =99

To determine

b)

To estimate:

The distance traveled during 1- minute time period using the velocities at the end of the time periods

To determine

c)

To explain:

Are estimates in part ‘a’ and part ‘b’ upper or lower estimates?

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