How to find when a particle is at rest from a position graph

The video tutorial discusses the conditions under which a particle is at rest, focusing on the concept of slope and its relation to motion. It explains that a particle is at rest when the slope is zero, particularly on the interval from zero to two. The tutorial also addresses the concept of instantaneous change in direction and the challenges of differentiating at sharp corners, where the derivative is undefined. The key takeaway is understanding the relationship between slope, rest, and motion in particle dynamics.

How does an instantaneous change affect the particle's state of rest?

What happens to the particle's motion between the interval of 0 to 2?