Chapter 2, Problem 74A

To determine

Whether it is possible to have an object’s position-time graph as a horizontal line or a vertical line.

Explanation of Solution

Introduction:

Two situation of object’s position versus time graph is provided, namely horizontal line graph and vertical line graph.

The expression for the average velocity $\left(\overline{v}\right)$ of an object or slope of object’s position versus time graph is as follows:

  $\overline{v}=\frac{\Delta x}{\Delta t}$

Here, $\Delta x$ represents the change in position of object (measured along vertical axis) and $\Delta t$ represents the time interval (measured along horizontal axis).

The slope of the position versus time graph of the object represents the average velocity of the object.

From the expression for the velocity $\left(\overline{v}\right)$ of an object or slope of object’s position versus time graph,

The object’s position versus time graph with a horizontal line indicates that the slope of the graph is zero (average velocity is zero). The position of the object remains constant with time.

Hence, the object’s position versus time graph with a horizontal line is possible for an object which is not moving with time.

The object’s position versus time graph with a vertical line indicates that the slope of the graph is infinite (average velocity is infinity). For this to happen, the object should move with infinite speed which is impossible.

Hence, the object’s position versus time graph with a vertical line is not possible.

Conclusion:

Thus, it is possible to have an object’s position-time graph as a horizontal line in case of non-moving object. On the other hand, it is impossible to have an object’s position-time graph as a vertical line as an object cannot move with infinite speed.