Chapter 2, Problem 51A

To determine

The position-time graph for the motion of walker and the runner.

Explanation of Solution

Introduction: Position time graph is plotted between the change in the position of an object (along the $x$ axis) and the time interval (along the $y$ axis). The slope of the this graph represents the average velocity of the object.

Consider a walker and a runner who leave the front door at the same time and moves in same direction. Hence, their point of origin is same.

Both the walker and runner move with different constant velocity.

As the velocity is constant for both the walker and the runner, the position time graph for both will be straight lines passing through the origin, each with different slopes.

Higher the velocity of a person, steeper will be the slope of the person’s position-time graph. It is obvious that the velocity of the runner will be more than that of the walker. Hence, the slope of the position time graph for the runner will be steeper in comparison to the walker.

Sketch the position-time graph for the runner and the walker as shown below:

  

Conclusion:

Thus, the position time graph for both walker and the runner will be straight lines with different slopes. The slope of the position time graph for the runner will be steeper in comparison to that of the walker.