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

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

(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.

(a)

To determine

To Estimate:

The distance travelled by the car using the velocities at the beginning of time intervals.

Explanation

Given information:

The number of intervals n=6.

Each interval value is Δt=10sec.

Calculation:

The expression to find the total distance travelled by the car (Ln) using the velocities at the beginning of time intervalsis shown below:

Ln=v(t0)Δt+v(t1)Δt+...+v(tn1)Δt (1)

Here, the velocity at time t0 is v(t0), the time interval is Δt, the time velocity t1 is v(t1), and the time velocity tn1 is v(tn1).

Substitute 6 for n in Equation (1).

L6=v(t0)Δt+v(t1)Δt+v(t2)Δt+v(t3)Δt+v(t4)Δt+v(t5)Δt (2)

Substitute 182.9 mi/h for v(t0), 10 sec for Δt, 168.0 mi/h for v(t1), 106.6 mi/h for v(t2), 99.8 mi/h for v(t3), 124.5 mi/h for v(t4), and 176.1 mi/h for v(t5) in Equation (2).

L6=[(182

(b)

To determine

To Estimate:

The distance travelled by the car using the velocities at the end of time intervals.

(c)

To determine

To Check:

The upper or lower estimates are obtained in part (a) and part (b).

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