   Chapter 10.5, Problem 85E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Velocity If a stone is dropped from a height of 400 feet, its height after t seconds is given by s = 400 − 16 t 2 .a. Find its average velocity over the period [ 2 , 4 ] .b. Estimate its instantaneous velocity at time t = 4 . [HINT: See Example 3.]

(a)

To determine

To calculate: The average velocity of the stone which is dropped at the height of 400m in time interval [2,4] provided that the height after t seconds is expressed as s=40016t2.

Explanation

Given information:

The stone is dropped at the height of 400m, the height after t seconds is expressed as s=40016t2.

Formula used:

The average rate of change of function f(x) is:

Average rate of change=ΔfΔt

Calculation:

Consider the function for height after t seconds, s=40016t2.

Evaluate the change in height from t=2 to t=4

Δs=s(4)s(2)

Evaluate the value of s(4),

s=40016t2s(4)=40016(4)2=40016(16)=144

Evaluate the value of s(2)

(b)

To determine

To calculate: The instantaneous velocity of the stone which is dropped at the height of 400m at t=4sec provided that the height after t seconds is expressed as s=40016t2.

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