From the graph, we can analyze the motion of the particle by observing the slope of the graph at different intervals.

1. Particle Moving to the Right: The particle moves to the right when the position $s$ increases over time $t$. This corresponds to segments where the graph has a positive slope (increasing).

   • From $t = 0$ to $t = 1$ (positive slope)
   • From $t = 5$ to $t = 6$ (positive slope)

   So, the particle is moving to the right during:

   • $(0, 1)$
   • $(5, 6)$

2. Particle Moving to the Left: The particle moves to the left when the position $s$ decreases over time $t$, corresponding to segments with a negative slope (decreasing).

   • From $t = 2$ to $t = 3$ (negative slope)

   So, the particle is moving to the left during:

   • $(2, 3)$

Answers:

• Moving to the right: $(0, 1)$, $(4, 6)$
• Moving to the left: $(2, 3)$

Would you like further details or clarifications on this?

Here are 5 related questions to consider:

1. At what times is the particle stationary (i.e., no movement)?
2. How far does the particle travel in total?
3. What is the average velocity of the particle between $t = 0$ and $t = 6$?
4. Can you determine the instantaneous velocity at $t = 1$?
5. How does the motion of the particle differ between $t = 3$ and $t = 5$?

Tip: The slope of a position-time graph gives the velocity at any point. A positive slope indicates forward motion, while a negative slope indicates backward motion.