The velocity of a particle is zero at t=0

Options

A. The accelerationat t=0 must be zero
B. the acceleration at t=0 maybet zero
C. If the acceleratin is zero from t=0 to t=10 s, the speed is also zero in this interval.
D. If the speed is zer4o from t=0 to t=10 s the acceleration is zero in this interval.

Answer

To solve the question regarding the velocity and acceleration of a particle at time \( t = 0 \), we will analyze each option provided in the question step by step.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We know that the velocity of the particle at \( t = 0 \) is \( 0 \). This means that the particle is at rest at that moment.

2. **Analyzing Option 1**:
- Option 1 states: "The acceleration at \( t = 0 \) must be \( 0 \)".
- This statement is **false**. Although the velocity is \( 0 \), the acceleration can be non-zero. For example, in the case of a free-falling object, the initial velocity is \( 0 \) but the acceleration due to gravity is \( 9.8 \, \text{m/s}^2 \).

3. **Analyzing Option 2**:
- Option 2 states: "The acceleration at \( t = 0 \) may be \( 0 \)".
- This statement is **true**. The acceleration can be \( 0 \) in certain situations, such as when an object is at rest on the ground with no external forces acting on it.

4. **Analyzing Option 3**:
- Option 3 states: "The acceleration is \( 0 \) from \( t = 0 \) to \( t = 10 \) seconds".
- This statement is also **true**. If the acceleration is \( 0 \) during this interval and the initial velocity is \( 0 \), then the velocity remains \( 0 \) throughout this time, as per the equation \( v = u + at \).

5. **Analyzing Option 4**:
- Option 4 states: "If the speed is \( 0 \) from \( t = 0 \) to \( t = 10 \) seconds, the acceleration in the interval is \( 0 \)".
- This statement is **true** as well. If the speed is \( 0 \) and the initial velocity is \( 0 \), then the only way for the velocity to remain \( 0 \) is if the acceleration is also \( 0 \).

### Conclusion:
- From the analysis, we conclude that:
- Option 1 is **false**.
- Option 2 is **true**.
- Option 3 is **true**.
- Option 4 is **true**.

### Final Answer:
- The correct options are **2, 3, and 4**.