Explanation:

When a particle moves with uniform velocity, it means that its speed and direction of motion remain constant over time. In other words, the particle is not accelerating.

Uniform Velocity:
- Uniform velocity refers to a situation where an object travels in a straight line with a constant speed.
- The magnitude (speed) and direction of the velocity remain constant throughout the motion.
- The object covers equal distances in equal intervals of time.

Acceleration:
- Acceleration is the rate of change of velocity with respect to time.
- If the velocity of an object changes, either in magnitude or direction or both, it is said to be accelerating.
- Acceleration can be positive (increasing velocity), negative (decreasing velocity), or zero (constant velocity).

Explanation of options:
a) Its speed is zero:
- If the particle has zero speed, it would not be moving at all.
- However, the question states that the particle is moving with uniform velocity, which means its speed is constant and not zero.
- Therefore, option (a) is incorrect.

b) Its acceleration is zero:
- If the particle is moving with uniform velocity, it means its speed and direction are not changing.
- Since acceleration is the rate of change of velocity, if the velocity is constant, the acceleration is zero.
- Therefore, option (b) is correct.

c) Its acceleration is opposite to the velocity:
- If the acceleration is opposite to the velocity, it means the particle is decelerating (slowing down) or changing direction.
- However, in the given scenario of uniform velocity, the particle's speed and direction remain constant.
- Therefore, option (c) is incorrect.

d) Its speed may be variable:
- The statement that the particle is moving with uniform velocity means its speed is constant.
- If the speed is constant, it cannot be variable.
- Therefore, option (d) is incorrect.

Conclusion:
The correct statement about the motion of a particle that is moving with uniform velocity is that its acceleration is zero (option b).