To understand the directions of an object's velocity and acceleration vectors when the object moves in a circular path with a constant speed, let's analyze the nature of circular motion:
1. Circular Motion with Constant Speed:
- When an object moves in a circular path with a constant speed, it is undergoing uniform circular motion.
- In uniform circular motion, the magnitude of the velocity remains constant, but its direction continuously changes as the object moves around the circle.
2. Velocity Vector:
- The velocity vector of an object moving in a circular path is always tangent to the circular path at any point. This means the velocity is directed along the tangent line at the object's position on the circumference of the circle.
3. Acceleration Vector:
- Even though the object's speed is constant, its changing direction means it is accelerating. This acceleration is known as centripetal acceleration.
- The centripetal acceleration vector always points towards the center of the circular path. Mathematically, centripetal acceleration is given by [tex]\( \vec{a} = \frac{v^2}{r} \)[/tex] where [tex]\( v \)[/tex] is the constant speed and [tex]\( r \)[/tex] is the radius of the circular path.
4. Direction Comparison:
- Since the velocity vector is tangent to the circle and the acceleration vector points towards the center, the two vectors are perpendicular to each other at any point along the path.
Thus, the correct answer is:
D. The vectors are perpendicular.
