Chapter 2.1, Problem 7E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

The table shows the position of a motorcyclist after accelerating from rest.

(a) Find the average velocity for each tune period:

(i) [2, 4]

(ii) [3, 4]

(iii) [4, 5]

(iv) [4, 6]

(b) Use the graph of *s as* a function of *t* to estimate the instantaneous velocity when *t =* 3.

(a)

To determine

**To find:** The average velocity for given time periods.

Explanation

**Formula used:**

The average velocity over the time interval

**Calculation:**

**Section-(i)**

Obtain the average velocity over the time interval [2, 4].

Substitute

From the given table, it is observed that,

(i) When

(ii) When

Thus, the average velocity over the time interval [2, 4] is computed as follows.

Therefore, the average velocity over the time interval [2, 4] is

**Section-(ii)**

Obtain the average velocity over the time interval [3, 4].

Substitute

From the given table, it is observed that,

(i) When

(ii) When

Thus, the average velocity over the time interval [3, 4] is computed as follows.

(b)

To determine

**To estimate:** The instantaneous velocity when

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