Which of the following describes the relationship between velocity and acceleration in non-uniform curvilinear motion? A) The velocity and acceleration vectors are always parallel B) The acceleration is always tangent to the curve of motion (C) The velocity and acceleration vectors are always perpendicular D) The velocity and acceleration vectors can have both tangential and normal components
The correct answer and explanation is:
Correct Answer: D) The velocity and acceleration vectors can have both tangential and normal components
Explanation:
In non-uniform curvilinear motion, an object moves along a curved path with changing speed. Unlike uniform circular motion (constant speed), non-uniform motion involves changes in both direction and magnitude of velocity, leading to a more complex relationship between velocity and acceleration.
1. Velocity in Curvilinear Motion
Velocity is always tangent to the path of motion, indicating the direction the object is currently moving. Its magnitude represents the object’s speed.
2. Acceleration in Curvilinear Motion
Acceleration can be split into two components:
- Tangential acceleration: This component is along the direction of velocity and changes the magnitude (speed) of the velocity.
- Normal (or centripetal) acceleration: This component is perpendicular to the velocity vector, pointing toward the center of curvature of the path. It changes the direction of the velocity vector.
3. Combined Effect
In non-uniform curvilinear motion, both the direction and magnitude of velocity change. Therefore, the acceleration vector is not purely tangent or perpendicular to the path. It is a vector sum of tangential and normal components.
This means the acceleration vector can point in any direction depending on the curve and speed, and it is generally not parallel or perpendicular to the velocity vector at all times.
Why D is Correct
Option D correctly captures this complexity:
“The velocity and acceleration vectors can have both tangential and normal components.”
This comprehensive description fits all cases of non-uniform curvilinear motion, making it the most accurate and complete option.
Incorrect Options:
- A) Only true for straight-line acceleration with constant direction.
- B) Applies only to tangential acceleration, ignoring the normal component.
- C) True in uniform circular motion, but not in non-uniform motion.