Final answer:
The correct motion is A, where the ball's horizontal motion is constant since no external forces act horizontally after it is thrown, and the vertical motion is accelerated due to the constant force of gravity.
Step-by-step explanation:
When analyzing the motion of a ball in the absence of air resistance, we can observe that the ball exhibits two types of motion: horizontal and vertical. In the horizontal direction, once the ball is thrown, it moves with a constant velocity because there are no additional forces acting on it.
This means that the horizontal velocity is unaffected by gravity, which acts vertically. The graph of the horizontal velocity versus time would be a horizontal line, which indicates a constant velocity. Hence, the horizontal motion of the ball is constant.
In the vertical direction, however, the ball is affected by gravity from the moment it is released. Gravity causes the ball to accelerate downwards, and as a result, the ball gains speed in the vertical direction as it falls. Therefore, the vertical motion is accelerated, with the acceleration due to gravity usually being approximately 9.81 m/s2 downwards. A graph of the ball's vertical acceleration versus time would show a horizontal line at the value of the acceleration due to gravity, indicating that the vertical acceleration is constant over time.
In conclusion, the correct option is A. The horizontal motion of the ball is constant, and the vertical motion is accelerated. This is under the idealized conditions where air resistance is neglected. In reality, air resistance would affect both motions, but this factor is not included in the given scenario.