Final answer:
The x-component of a velocity vector, denoted as Vx, represents an object's velocity along the x-axis and is calculated using the formula Vx = v cos(θ). For an object moving solely along the x-axis, the x-component equals the magnitude of the entire velocity vector. If no horizontal acceleration is present, Vx remains constant.
Step-by-step explanation:
The x-component of the velocity vector is a representation of an object's velocity in the horizontal direction within a two-dimensional space. When dealing with motion, especially that of a rotating disk, it is common in physics to break down the motion into components along the axes of a coordinate system. The x-component, often denoted as Vx, depicts how fast the object is moving along the x-axis.
To calculate the x-component of the velocity of an edge of a rotating disk, one can use the relation Vx = v cos(θ), where 'v' is the magnitude of the velocity and 'θ' is the angle of the velocity vector relative to the horizontal axis. If the object is initially moving along the x-axis, then θ is zero and thus cos(0) equals 1, resulting in Vx = v, meaning the velocity vector lies entirely along the x-axis.
For situations where there is no horizontal acceleration, such as when an object moves horizontally at a constant speed or when the only forces acting on it are vertical (like gravity), the x-component of the velocity remains constant. This principle helps in solving problems regarding projectile motion or the motion of objects on a frictionless surface, where the horizontal component of the velocity does not change over time.