Final answer:
The direction of the ball's velocity at point x would depend on the initial direction of motion. If it was kicked or thrown to the right, the horizontal velocity would be to the right. The ball's velocity will be zero at the trajectory's peak, and the direction of velocity will reverse as it begins to fall back down.
Step-by-step explanation:
To determine the direction of the ball's velocity at point x without knowing the specific context, a general principle can be applied. If the ball is in free-fall or projectile motion and point x is at the peak height of its trajectory, the ball's vertical velocity will be zero, and its horizontal velocity will be pointing in the direction it was initially kicked or thrown.
In the absence of friction, the horizontal velocity remains constant throughout the motion. Therefore, if the ball was initially kicked or thrown to the right, the velocity at point x will be to the right.
A ball thrown straight up into the air will have its velocity at the apex (the highest point) reduced to zero before it starts to fall back down, changing its direction. The acceleration due to gravity is negative on the way up (opposing the motion) and positive on the way down (in the same direction as the motion), so the acceleration due to gravity does maintain the same sign both ways.
In projectile motion, the vertical acceleration versus time graph shows a constant acceleration due to gravity, while the horizontal velocity-versus-time graph remains constant if air resistance is neglected. This is because gravity does not affect horizontal motion in the absence of other forces.