(A) : The directions of velocity and acceleration can be in any way.
(R) : The direction of acceleration depends on the direction of force, but not on the direction of velocity.

Both (A) and (R) are true, and (R) is the correct explanation of (A).

In physics, both velocity and acceleration are vector quantities, meaning they have both magnitude and direction. The relationship between these two vectors depends on the nature of the object's motion:

1. Direction of Velocity and Acceleration:

The directions of velocity and acceleration can vary based on the object's motion:

• In the Same Direction: If an object is speeding up, the acceleration vector points in the same direction as the velocity vector. For example, a car accelerating forward has both velocity and acceleration in the forward direction.
• Opposite Directions: If an object is slowing down, the acceleration vector points opposite to the direction of the velocity vector. For instance, a car braking has a velocity vector pointing forward and an acceleration vector pointing backward.
• Perpendicular Directions: In uniform circular motion, the velocity vector is tangent to the path, while the acceleration vector (centripetal acceleration) points toward the center of the circle, perpendicular to the velocity vector. This means the object is constantly changing direction but not speed.

2. Direction of Acceleration and Force:

The direction of acceleration is determined by the direction of the net force acting on the object:

• Newton's Second Law: This law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, F = ma, where F is the net force, m is the mass, and a is the acceleration. The acceleration vector points in the same direction as the net force vector.

Therefore, both statements (A) and (R) are true. The direction of acceleration depends on the direction of the net force acting on the object, which in turn influences the object's velocity. This relationship explains how acceleration can be in any direction relative to velocity, depending on the nature of the object's motion and the forces involved.