Chapter 2, Problem 52A

To determine

The quantity depicted by the slope of a position-time graph.

Answer to Problem 52A

Average velocity

Explanation of Solution

Introduction:

The average velocity of a particle is given by

  $\overline{v}=\frac{\Delta d}{\Delta t}=\frac{d_{final}-d_{initial}}{t_{final}-t_{initial}}$

Where $d$ is the displacement of a particle while $t$ is the time taken.

Now, when the time taken $\left(t\right)$ by a particle is presented on the x-axis and the position of a particle with respect to a reference point $\left(d\right)$ is marked on the y-axis of a x-y graph, then the slope of such graph will be

  $\text{slope}=\frac{\Delta y}{\Delta x}=\frac{\Delta d}{\Delta t}$

Using the above-mentioned formula of average velocity

  $\text{slope}=\overline{v}$

Conclusion:

Hence, the slope of a position-time graphdepicts the average velocity of a particle.