The velocity of a particle is zero at t = 0.
(a) The acceleration at t= 0 must be zero.
(b) The acceleration at t = 0 may be zero.
(c) If the acceleration is zero from t = 0 to t=10s, the speed is also zero in this interval.
(d) If the speed is zero from t=0 to t=10 s the acceleration is also zero in this interval.

Options

A. a, b & d are correct
B. b,c & d are correct
C. a, c & d are correct
D. a, b & c are correct

Answer

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

### Step-by-Step Solution:

1. **Statement (a): The acceleration at \( t = 0 \) must be zero.**
- **Analysis:** This statement is incorrect. Acceleration is defined as the rate of change of velocity. Just because the velocity is zero at \( t = 0 \) does not imply that the acceleration must also be zero. The velocity could change immediately after \( t = 0 \), leading to a non-zero acceleration.
- **Conclusion:** **False**

2. **Statement (b): The acceleration at \( t = 0 \) may be zero.**
- **Analysis:** This statement is correct. While the acceleration does not have to be zero, it is possible for it to be zero. For example, if the particle remains at rest (velocity = 0) and does not start moving, the acceleration can indeed be zero.
- **Conclusion:** **True**

3. **Statement (c): If the acceleration is zero from \( t = 0 \) to \( t = 10 \, s \), the speed is also zero in this interval.**
- **Analysis:** This statement is true. If the acceleration is zero, it means that the velocity is constant. Since the velocity is zero at \( t = 0 \), it must remain zero for the entire interval from \( t = 0 \) to \( t = 10 \, s \). Therefore, the speed remains zero throughout this time.
- **Conclusion:** **True**

4. **Statement (d): If the speed is zero from \( t = 0 \) to \( t = 10 \, s \), the acceleration is also zero in this interval.**
- **Analysis:** This statement is also true. If the speed is zero and does not change during the interval, it implies that the velocity is constant (in this case, constant at zero). Since there is no change in velocity, the acceleration must be zero.
- **Conclusion:** **True**

### Final Answers:
- (a) False
- (b) True
- (c) True
- (d) True