Final answer:
The x-component of velocity remains unchanged when an object with a constant x-velocity experiences acceleration in the y direction, as motion in one direction is independent of motion in a perpendicular direction. This principle applies to concepts such as projectile motion and uniform circular motion.
Step-by-step explanation:
If an object has a constant x-component of velocity and suddenly experiences an acceleration in the y direction, the x-component of its velocity does not change. According to the principles of Physics, specifically Newton's first law of motion, an object's state of motion in one direction is independent of its state of motion in a perpendicular direction unless acted upon by an external force in that direction. Thus, adding acceleration in the y direction will not affect the velocity component in the x direction.
For example, when considering projectile motion, the only force acting is gravity, which pulls objects down in the y direction. There is no force acting in the x direction (assuming air resistance is negligible), so the x-component of the object's velocity remains constant. Similarly, if a constant, nonzero force is applied at an angle to the x direction, the x-component of the velocity changes only if the force has a component in the x direction.
An object in uniform circular motion is indeed accelerating because, while the speed may be constant, the direction of the velocity is continually changing, which constitutes acceleration. And when considering Newton's first law, it states that an object will remain at a constant velocity unless acted on by an external force; thus, if your car moves at a constant velocity down the street, it implies that no net external force is acting on it, and the first law applies.