Final answer:
Time (t) is the variable shared between the kinematic equations for the two dimensions.
Step-by-step explanation:
In kinematics, the equations governing motion in two dimensions involve variables like displacement (s), initial velocity (v), final velocity (v'), acceleration (a), and time (t). Time is the only variable common to both dimensions, horizontally and vertically, as it remains constant regardless of direction. Each dimension's motion can be treated separately using its respective set of equations, but time remains a unifying factor. For instance, in projectile motion, while horizontal and vertical motions have distinct equations, both incorporate time to determine the overall motion.
When an object moves in two dimensions, time doesn't change between the horizontal and vertical motions. It's an intrinsic property of the motion itself, unaffected by direction. For example, when calculating the time an object takes to reach the maximum height in a projectile motion, the time taken in the vertical motion is the same as the time taken in the horizontal motion. This consistency in time allows us to link the two dimensions of motion and analyze the object's trajectory accurately.
Therefore, while displacement, velocity, and acceleration may differ between horizontal and vertical motions, time remains a constant link between these dimensions. Understanding this shared variable is crucial in solving problems involving motions in two dimensions, enabling a comprehensive analysis of an object's path and behavior in both the x and y directions.