Chapter 2.7, Problem 11E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

(a) A particle starts by moving to the right along a horizontal line; the graph of its position function is shown in the figure. When is the particle moving to the right? Moving to the left? Standing still?

(b) Draw a graph of the veloc.ity function.

(a)

To determine

**To state:** The position at which the particle is moving to the right, moving to the left and standing still on the time intervals.

Explanation

**Formula used:**

The average velocity over the time interval

**Note 1:** The average velocity is same as the instantaneous velocity when the particle is moving along a straight line.

**Note 2:** The particle is moving to the right when the velocity is positive.

**Note 3:** The particle is moving to the left when the velocity is negative.

**Note 4:** The particle is standing still when the velocity is zero.

**Calculation:**

At the time interval (0, 1):

From the given graph, it is observed that the straight line is passing through the points (0, 0) and (1,3).

Substitute (0, 0) for

Thus, the average velocity of the particle moving along a straight line is

By Note 1, the velocity of the particle on the time interval (0, 1) is

By Note 2, the particle is moving to the right on the time interval (0, 1) since the velocity is positive.

Thus, the particle is moving to the right when

At the time interval (1, 2):

From the given graph, it is observed that the straight line is passing through the points (1, 3) and (2,3).

Substitute (1, 3) for

Thus, the average velocity of the particle moving along a straight line is

By Note 1, the velocity of the particle on the time interval (1, 2) is

By Note 4, the particle is standing still on the time interval (1, 2), since the velocity is zero.

Thus, the particle is standing still when

At the time interval (2, 3):

From the given graph, it is observed that the straight line is passing through the points (2, 3) and (3,1)

(b)

To determine

**To sketch:** The graph of the velocity function.

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