Final answer:
The variable connecting a projectile's motion along the X and Y axis is time. Acceleration affects projectile motion only in the Y-axis due to gravity while X-axis motion has zero acceleration. Kinematic equations involve acceleration, displacement, time, and velocity.
Step-by-step explanation:
The only variable that connects the motion of a projectile along the X and Y axis is time. This is because the motion of a projectile can be analyzed by breaking it into two independent one-dimensional motions along the vertical (Y-axis) and horizontal (X-axis). The acceleration due to gravity affects the projectile's motion in the Y-axis, which is why the rate of change of velocity, called acceleration, is constant and non-zero in the Y-direction but zero in the X-direction for a projectile in motion, assuming air resistance is negligible. From a velocity vs. time graph, we could determine the acceleration among other pieces of information. When considering the four variables found in the kinematic equations, those are acceleration, displacement, time, and velocity.