Final answer:
A ball is subject to the force of gravity, but its path is not always a straight line nor are its speed and acceleration constant due to various external forces. The ball's path, speed, and acceleration change in response to external forces, particularly gravity, which causes it to accelerate downward during free fall.
Step-by-step explanation:
When analyzing the ball's motion, one must consider the forces acting on it and the principles of mechanics that govern its path. Statement (a) is correct; a ball is always subject to the force of gravity, which acts downward towards the center of the Earth and affects its motion. However, the ball does not always follow a straight-line path as mentioned in statement (b); its path depends on the forces acting on it and the initial conditions of its motion. For instance, when a ball is thrown or launched, it follows a parabolic trajectory under the influence of gravity, which is not a straight line.
Statement (c) is incorrect because the ball’s motion can definitely be affected by external forces such as air resistance, friction, or applied forces. Finally, statement (d) is not accurate; a ball's speed and acceleration are not constant throughout its motion except under specific, idealized conditions, like when it is moving in vacuum with no external forces aside from gravity. The speed changes as the ball moves along its trajectory, and acceleration changes direction and magnitude unless it's in free fall in a vacuum.
Considering Newton's laws of motion, particularly the first law, we know a body in motion tends to remain in motion at a constant velocity unless acted upon by a net external force. This would apply to a ball moving in space but not within Earth's atmosphere where gravity and potentially air resistance apply. For an object in free fall, only gravity acts on it and it accelerates downwards.
The influence of gravity on a ball's vertical motion can be visually represented by its vertical acceleration versus time graph, which would show a constant acceleration downward. This is consistent with the acceleration due to gravity being a constant near the Earth's surface. In the absence of air resistance, the horizontal velocity of a ball is constant after it is thrown, which could be represented by a flat graph of horizontal velocity over time. However, real-world conditions such as air resistance and the potential for other external forces mean that the motion of actual balls may deviate from these idealized models.