Which of the following statements is not correct?

Options

A. 1. The zero velocity of a body at any instant does not necessarily impy zero acceleration at that instant.
B. 2. The kinematic equation of motions are true only for motion in which the magnitude and the direction of acceleration are constants during the couse of motion.
C. 3. The sign of acceleration tells us whether the particle's speed is increasing or decreasing.
D. 4. all of these

Explanation

To solve the question of identifying which statement is not correct, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement 1: "The zero velocity of a body at any instant does not necessarily imply zero acceleration at that instant."**
- **Analysis:** This statement is true. A body can have zero velocity while still experiencing acceleration. For example, a ball thrown upwards reaches a velocity of zero at its highest point, but it is still accelerating downwards due to gravity. Thus, this statement is correct.

2. **Statement 2: "The kinematic equations of motion are truly only for motion in which the magnitude and the direction of acceleration are constant during the course of motion."**
- **Analysis:** This statement is also true. The kinematic equations apply only when acceleration is constant. If acceleration varies, these equations cannot be applied directly. Therefore, this statement is correct.

3. **Statement 3: "The sign of acceleration tells us whether the particle's speeding is increasing or decreasing."**
- **Analysis:** This statement is misleading and therefore incorrect. The sign of acceleration indicates the direction of the acceleration vector, but it does not directly tell us whether the speed of the particle is increasing or decreasing. For example, if an object is moving in the positive direction and has a negative acceleration, its speed is decreasing. Conversely, if it is moving in the negative direction with negative acceleration, its speed is increasing. Thus, this statement is not correct.

4. **Statement 4: "The kinematic equations can be used for any type of motion."**
- **Analysis:** This statement is incorrect. The kinematic equations are only applicable under specific conditions, namely when acceleration is constant. Therefore, this statement is also not correct.

### Conclusion:
The statement that is not correct is **Statement 3**: "The sign of acceleration tells us whether the particle's speeding is increasing or decreasing."