if angle a b/w acceleration and velocity vector is 90

a)straight path with retardation

b)straight path with acceleration

c)curvillinear path with acceleration

d)curvillinear path with retardation

When the angle between the acceleration vector and the velocity vector is 90 degrees, it indicates a specific relationship between the motion of an object. This scenario typically occurs when the acceleration is perpendicular to the velocity, which can happen in various contexts. Let's break down the options you've provided to see which one fits this condition best.

Understanding the Motion Scenarios

To analyze the options, we need to consider what it means for acceleration to be perpendicular to velocity:

• Acceleration: This vector indicates the rate of change of velocity.
• Velocity: This vector represents the speed and direction of an object's motion.

When acceleration is perpendicular to velocity, it does not change the speed of the object but alters its direction. This is a key characteristic of uniform circular motion, where an object moves along a curved path while maintaining a constant speed.

Evaluating Each Option

• a) Straight path with retardation: In this case, the object is slowing down, which means the acceleration vector is directed opposite to the velocity vector. The angle between them would be 180 degrees, not 90 degrees.
• b) Straight path with acceleration: Here, the object is speeding up in a straight line. The acceleration vector is in the same direction as the velocity vector, resulting in an angle of 0 degrees, not 90 degrees.
• c) Curvilinear path with acceleration: This scenario can involve acceleration that is perpendicular to the velocity vector. For instance, if an object moves in a circular path, the acceleration (centripetal acceleration) points towards the center of the circle while the velocity is tangent to the path. Thus, the angle between them is indeed 90 degrees.
• d) Curvilinear path with retardation: In this case, if the object is slowing down while moving along a curved path, the acceleration vector would still not be perpendicular to the velocity vector. Instead, it would have a component that opposes the direction of motion, resulting in an angle that is not 90 degrees.

Conclusion on the Correct Option

Based on this analysis, the correct answer is c) curvilinear path with acceleration. In this scenario, the acceleration is perpendicular to the velocity, allowing the object to change direction while maintaining a constant speed, which is characteristic of circular motion or any curved trajectory where the speed remains constant.

Understanding these relationships between acceleration, velocity, and the path of motion is crucial in physics, particularly in dynamics and kinematics. It helps us predict how objects will behave under various forces and conditions.