Final answer:
In physics, the motion of a point-like object in a Cartesian coordinate system can be understood by decomposing its velocity into components. This description typically involves analyzing the object's trajectory using separate horizontal and vertical equations of motion.
Step-by-step explanation:
The question relates to the topic of kinematics in physics, specifically describing motion in a Cartesian coordinate system. In the scenario presented, a point-like object has a velocity with only an x-component that varies with time, while the y and z-components of the velocity are zero. When data or functions for position or velocity components along the curvilinear paths are known, one can determine the direction of velocity as well as its components (vx and vy) by resolving the object's position and velocity into horizontal and vertical components. A practical example is the trajectory of a particle which can be described by the position and velocity vectors over time. For instance, if vx is the horizontal velocity, we equate vx = v cos θ, where v is the magnitude of the velocity, and θ its direction with respect to the horizontal axis.
Analysis of the projectile's motion will include horizontal and vertical components, where equations of motion can be applied separately. For horizontal motion (ax=0), velocity in the x-direction remains constant, while for vertical motion, one must consider the acceleration due to gravity (ay = -g).