In a projectile motion the velocity
a) is always perpendicular to the acceleration
b) is not always perpendicular to the acceleration
c) is perpendicular to the acceleration for one instant only
d) is perpendicular to the acceleration for two instants.

Options

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

Answer

To solve the question regarding the relationship between velocity and acceleration in projectile motion, we will analyze the motion step by step.

### Step-by-Step Solution:

1. **Understanding Projectile Motion**:
- In projectile motion, an object is thrown into the air and moves under the influence of gravity. The motion can be analyzed in two dimensions: horizontal and vertical.

2. **Components of Velocity**:
- The velocity of the projectile can be broken down into two components:
- **Horizontal Component (Vx)**: This remains constant throughout the motion because there is no horizontal acceleration (assuming air resistance is negligible).
- **Vertical Component (Vy)**: This changes due to the acceleration caused by gravity (g), which acts downwards.

3. **Acceleration in Projectile Motion**:
- The only acceleration acting on the projectile is the gravitational acceleration (g), which acts vertically downward. Thus, the acceleration vector is always directed downward.

4. **Analyzing the Relationship**:
- At the peak of the projectile's trajectory, the vertical component of the velocity (Vy) becomes zero, while the horizontal component (Vx) remains constant. At this instant, the velocity vector is horizontal, and the acceleration vector is vertical, making them perpendicular to each other.
- At other points in the trajectory, the velocity vector has both horizontal and vertical components, and they are not perpendicular to the acceleration vector.

5. **Conclusion**:
- The velocity is not always perpendicular to the acceleration. It is perpendicular at one specific instant (the peak of the trajectory) when the vertical component of the velocity is zero. Therefore, the correct statements are:
- **B**: The velocity is not always perpendicular to the acceleration.
- **C**: The velocity is perpendicular to the acceleration for one instant only.

6. **Final Answer**:
- The correct option is **B and C**.