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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?

When is the particle speeding up? Slowing down? Enter using interval notation.

Learn how to determine when a particle is speeding up or slowing down using interval notation. This problem covers essential calculus concepts such as velocity, acceleration, and sign analysis. Suitable for high school or college students studying calculus.

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