Fundamentals of Physics Extended
10th Edition
ISBN: 9781118230725
Author: David Halliday, Robert Resnick, Jearl Walker
Publisher: Wiley, John & Sons, Incorporated

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Textbook Question
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Chapter 2, Problem 1Q

Figure 2-16 gives the velocity of a particle moving on an x axis. What are (a) the initial and (b) the final directions of travel? (c) Does the particle stop momentarily? (d) Is the acceleration positive or negative? (e) Is it constant or varying?

Figure 2-16 Question 1.

To determine

To find:

a) Initial direction of travel.

b) Final direction of travel.

c) Does the particle stop momentarily?

d) Is the acceleration positive or negative?

e) Is the acceleration constant or varying?

Solution:

a) Initial direction of travel is negative.

b) Final direction of travel is positive.

c) The particle stops momentarily.

d) The acceleration is positive.

e) The acceleration is constant.

### Explanation of Solution

1) Concept:

After reading the graph, we can say that the Initial direction of travel is negative. As compared to that final direction of travel is positive.

As for an instance the velocity of the particle is zero, it indicates that the particle stops momentarily.

From the graph, we can say that the acceleration is positive and constant as the graph is a straight line and ascending in positive direction.

2) Given:

Graph in Fig 2.16.

3) Calculations:

a) When we look at the graph, it is starting below the x-axis, which states that the initial direction of travel would be negative.

b) When we look at the graph, it is ending above the x-axis, which states that the final direction of travel would be positive.

c) When we say it stops momentarily, it means the velocity of the particle is zero for a moment. When we look at the graph, the velocity is zero for one point, so we can say that the particle stops momentarily.

d) Now as the graph is moving from negative velocity to positive velocity, it means the velocity is increasing. From the above statement, we can say that the acceleration is positive.

e) As the graph is a straight line, the acceleration is constant.

Conclusion:

We have been given the graph of velocity vs time. From this graph, we can find the acceleration of the object by finding the slope of the graph. Looking at the nature of the graph, we can also conclude the direction of the acceleration and velocity at any given point.

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