Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 2.1, Problem 4E

To determine

To find: The speed of the object at t=4 seconds. Confirm the answer algebraically.

Expert Solution & Answer

Answer to Problem 4E

The speed of the object at t=4 seconds is 128 ft/sec .

Explanation of Solution

Given information:

An object is dropped from rest from the top of a building falls y=16t2 feet in first t seconds.

Calculation:

The instantaneous speed of an object at t=a seconds is the average speed from time t=a seconds to t=a+h seconds.

Use the formula for average speed.

s=ΔyΔt=y2−y1t2−t1

Substitute 4+h for t in the given equation for the distance travelled.

y2=16(4+h)2

Substitute 4 for t in the given equation for the distance travelled.

y1=16(4)2=16×16=256

Substitute these values in the formula for average speed.

s=y2−y1t2−t1=16(4+h)2−2564+h−4=16(4+h)2−256h

Substitute 0.0001 for h in the above expression for approximate speed.

s=16(4+h)2−256h=16(4+0.0001)2−2560.0001=16(4.0001)2−2560.0001=256.0128−2560.0001

Further simplify,

s=256.0128−2560.0001=0.01280.0001=128 ft/sec

So, the instantaneous speed of the object at t=4 seconds is approximately 128 ft/sec .

Use the formula for speed of the object algebraically.

s=y2−y1t2−t1=16(4+h)2−2564+h−4=16(4+h)2−256h=16(16+h2+8h)−256h

Further, simplify.

s=16(16+h2+8h)−256h=256+16h2+128h−256h=h(16h+128)h=16h+128

Substitute 0 for h for the exact instantaneous speed.

s=16h+128=16×0+128=128 ft/sec

Therefore, the speed of the object at t=4 seconds is 128 ft/sec .

Chapter 2.1, Problem 3E

Chapter 2.1, Problem 5E

Chapter 2 Solutions

Calculus: Graphical, Numerical, Algebraic

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The speed of the object at t = 4 seconds. Confirm the answer algebraically.