# Random displacement and velocity simulation

Oftentimes, the kinematics graphs that students see in their textbooks are very clean and simple. In nature, movement is often haphazard and to simulate such movement in one dimension, I generated this (https://physicstjc.github.io/sls/random-displacement/index.html) using ChatGPT 4o.

There is a drop-down menu that allows users to toggle between displacement and velocity graphs.

In a displacement-time graph, the displacement is plotted on the y-axis and time on the x-axis. A positive displacement represents a position to the right of the origin while a negative displacement is to its left. The slope of this graph represents the object’s velocity; a steeper slope indicates a higher velocity. A positive slope means the object is moving forward, a negative slope indicates it is moving backward, and a zero slope shows the object is at rest. For example, in uniform motion, the displacement-time graph is a straight line with a constant slope, reflecting constant velocity.

Conversely, in a velocity-time graph, velocity is on the y-axis and time on the x-axis. The area under the velocity-time graph represents the object’s displacement. Areas above the time axis denote positive displacement, while areas below indicate negative displacement.