The problem is asking when the particle is speeding up or slowing down, and it requires the answer in interval notation.

To determine when a particle is speeding up or slowing down, we typically look at the signs of both the velocity $v(t)$ and acceleration $a(t)$. Specifically:

• Speeding up: when velocity and acceleration have the same sign (either both positive or both negative).
• Slowing down: when velocity and acceleration have opposite signs (one positive and the other negative).

From your input:

• The interval $0 \geq t \geq 6$ appears to have some incorrect notation (it's not valid interval notation).
• For speeding up, the correct notation should involve when the velocity and acceleration are both positive or both negative.
• For slowing down, you would write the interval where one is positive and the other is negative.

Let's rephrase this and check the intervals using correct notation.

For example, if $0 \leq t \leq 6$ is meant, you would use interval notation $[0, 6]$ for speeding up.

Clarification:

1. Do you have the expressions for velocity $v(t)$ and acceleration $a(t)$?
2. Should the intervals be based on sign changes of velocity and acceleration?

Would you like to provide more details or equations so I can help you correct the intervals?