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.

Under what condition is a particle considered to be at rest?

• When the slope is positive

• When the slope is negative

• When the slope is undefined

• When the slope is zero

What happens to the particle at a sharp corner?

• The derivative is zero

• The derivative is undefined

• The derivative is negative

• The derivative is positive

Why can't the derivative be taken at a sharp corner?

• Because the slope is positive

• Because the slope is negative

• Because the slope is undefined

• Because the slope is zero

When is the particle at rest according to the final conclusion?

• When it is moving right

• When it is moving left

• When it is constant over an interval

• When it is accelerating

What is the significance of the interval from zero to two in the context of the particle's motion?

• The particle is changing direction

• The particle is decelerating

• The particle is at rest

• The particle is accelerating