Chapter 2.1, Problem 5E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

If a ball is thrown into the air with a velocity of 40 ft/s, its height in feet *t* seconds later is given by *y* = 40*t* – 16*t*^{2}.

(a) Find the average velocity for the time period beginning when *t* = 2 and lasting

(i) 0.5 seconds

(ii) 0.1 seconds

(iii) 0.05 seconds

(iv) 0.0 I seconds

(b) Estimate the instantaneous velocity when *t* = 2.

(a)

To determine

**To find:** The average velocity for the time period beginning when

Explanation

**Given:**

The velocity of the ball is

The height (in feet) of the ball after *t* seconds is

**Calculation:**

Obtain the average velocity over the time interval [*t, t + h*].

Obtain average velocity of the position function over the interval [2*,* 2*+h*].

Simplify further and obtain the average velocity as follows:

Thus, the average velocity of the position function

[2*,* 2*+h*] is,

**Section-(i):**

Obtain the average velocity for the time period beginning when

(b).

To determine

**To estimate:** The instantaneous velocity when

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P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-46RECh-2 P-47RECh-2 P-48RECh-2 P-49RECh-2 P-50RECh-2 P-51RECh-2 P-52RECh-2 P-53RECh-2 P-54RECh-2 P-1PCh-2 P-2PCh-2 P-3PCh-2 P-4PCh-2 P-5PCh-2 P-6PCh-2 P-7PCh-2 P-8PCh-2 P-9PCh-2 P-10PCh-2 P-11PCh-2 P-12PCh-2 P-13PCh-2 P-14P

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