Chapter 2, Problem 37RE

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8th Edition

James Stewart

ISBN: 9781305270336

Textbook Problem

The displacement (in meters) of an object moving in a straight line is given by *s* = 1 + 2t + *¼ t*^{2}, where *t* is measured in seconds.

(a) Find the average velocity over each time period.

(i) [l, 3]

(ii) [1, 2]

(iii) [ 1, 1.5]

(iv) [ 1, 1.1]

(b) Find the instantaneous velocity when *t* = 1.

(a)

To determine

**To find:** The average velocity of an object over the given time periods.

Explanation

**Given:**

The displacement (in meters) of an object is moving in a straight line.

The equation of a position function is *t* is measured in seconds.

**Formula used:**

The average velocity over the time interval

**Calculation:**

Obtain the average velocity of the particle over the time interval

Take the position function

Simplify further and obtain the value of average velocity as follows.

Thus, the average velocity of the particle over the time interval

**Section (i)**

Obtain the average velocity of the particle over the time interval

Consider

Substitute 1 for *a* and 2 for *h* in the average velocity,

Thus, the average velocity of the particle over the time interval

(b)

To determine

**To find:** The instantaneous velocity at

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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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