Chapter 3.1, Problem 2PP

a.

To determine

The time when the speed of the train is constant.

Explanation of Solution

Introduction:

A velocity time graph is one in which velocity is graphedon y axis and time on x axis. It shows the change in velocity with time. The slope of the graph provides the acceleration and the area under the graph provides the distance covered by the object.

As clearly shown in the graph, the value of the velocity plotted for the time between $5$ seconds to $15$ seconds is the same at $10\text{ m/s}$ . Hence, the speed of the train is constant between $5$ seconds to $15$ seconds.

Conclusion:

The speed of the train is constant between $5$ seconds to $15$ seconds.

b.

To determine

The time during which the train’s acceleration is positive.

Explanation of Solution

Introduction:

A velocity time graph is one in which velocity is graphedon y axis and time on x axis. It shows the change in velocity with time. The slope of the graph provides the acceleration and the area under the graph provides the distance covered by the object.

The slope of the velocity time graph gives the acceleration, which is the ratio of the change in y axis to the change in x axis. When the slope is positive, it shows positive acceleration. In this graph, the slope is positive from 0 to $5$ seconds. Hence, the train’s acceleration is positive from 0 to $5$ seconds.

Conclusion:

The train’s acceleration is positive from 0 to $5$ seconds.

c.

To determine

The time during which the train’s acceleration is the most negative.

Explanation of Solution

Introduction:

A velocity time graph is one in which velocity is graphedon y axis and time on x axis. It shows the change in velocity with time. The slope of the graph provides the acceleration and the area under the graph provides the distance covered by the object.

The slope of the velocity time graph gives the acceleration, which is the ratio of the change in y axis to the change in x axis. When the slope is negative, it shows negative acceleration. The greater the slope, the higher is the acceleration. In this graph, the slope is negative from $15$ seconds to $40$ seconds. The acceleration is the most negative from $15$ seconds to $20$ seconds.

Conclusion:

The acceleration is the most negative from $15$ seconds to $20$ seconds.