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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.1, Problem 7E

(a)

To determine

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

Expert Solution

(i) The average velocity over the time interval [2, 4] is

(ii) The average velocity over the time interval [3, 4] is

(iii) The average velocity over the time interval [4, 5] is

(iv) The average velocity over the time interval [4, 6] is

**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.

Therefore, the average velocity over the time interval [3, 4] is

**Section-(iii)**

Obtain the average velocity over the time interval [4, 5].

Substitute

From the table, it is observed that,

(i) When

(ii) When

Thus, the average velocity over the time interval [4, 5] is computed as follows.

Therefore, the average velocity over the time interval [4, 5] is

**Section-(iv)**

Obtain the average velocity over the time interval [4, 6].

Substitute

From the table, it is observed that,

(i) When

(ii) When

Thus, the average velocity over the time interval [4, 6] is computed as follows.

Therefore, average velocity over the time interval [4, 6] is

(b)

To determine

**To estimate:** The instantaneous velocity when

Expert Solution

The estimated instantaneous velocity when

Plot a curve using the points (0, 0), (1, 4.9), (2, 20.6), (3, 46.5), (4, 79.2), (5, 124.8) and (6, 176.7) as shown below in Figure 1.

Draw the slope of the tangent line at

The instantaneous velocity at

From Figure 2, the slope of the tangent line at (3, 46.5) is obtained below.

The estimated instantaneous velocity when