Choose the wrong statement .

Options

A. zero - velocity of a particle at any instant does not necessarily mean that its acceleration is zero
B. zero acceleration of a particle at any instant does not necessarily mean that its velocity is zero
C. if the seed a particle constant , its acceleration must be zero
D. none of the above

Answer

To solve the question of identifying the wrong statement, we will analyze each option provided in the question step by step.

### Step 1: Analyze the First Statement
**Statement 1:** "Zero velocity of a particle at any instant does not necessarily mean that acceleration is zero."

- This statement is **true**. A particle can have zero velocity while still experiencing acceleration. For example, when an object is dropped from a height, at the moment it is released, its velocity is zero, but it is still accelerating downwards due to gravity.

### Step 2: Analyze the Second Statement
**Statement 2:** "Zero acceleration of a particle at any instant does not necessarily mean that velocity is zero."

- This statement is also **true**. If the acceleration is zero, it means the velocity is constant. The velocity can be zero or it can be a non-zero constant value. For instance, a car moving at a constant speed of 2 m/s has zero acceleration, but its velocity is not zero.

### Step 3: Analyze the Third Statement
**Statement 3:** "If the speed of a particle is constant, its acceleration must be zero."

- This statement is **false**. A particle can have a constant speed while still having a non-zero acceleration if it is moving in a circular path (uniform circular motion). In this case, the speed remains constant, but the direction of the velocity changes, resulting in centripetal acceleration directed towards the center of the circular path.

### Conclusion
After analyzing all three statements, we conclude that the third statement is the wrong one.

### Final Answer
The wrong statement is: **"If the speed of a particle is constant, its acceleration must be zero."**

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