Final answer:
A ball thrown downward with a large starting velocity does not accelerate more rapidly than one dropped with no initial velocity, as both experience the same constant acceleration due to gravity, which is independent of initial movement.
Step-by-step explanation:
The question of whether a ball thrown downward with a large starting velocity will accelerate more rapidly than one that is dropped with no initial velocity pertains to the concepts of free fall and acceleration due to gravity. In the absence of air resistance, the acceleration of a free-falling object is constant and does not depend on the object's initial velocity. Whether a ball is dropped with no initial velocity or is thrown downward (or upward), it will experience the same constant acceleration of approximately 9.81 m/s2 downward, which is the acceleration due to gravity on Earth's surface. This acceleration is independent of any initial velocity the ball may have.
The significance of understanding free fall comes from the realization that the effect of gravity is the same regardless of an object's initial motion. Objects in free fall, whether moving up or down, experience a constant downward acceleration. Hence, a ball thrown downward with a large starting velocity will not accelerate more rapidly and will reach the ground with an increase in speed that corresponds to the gravitational acceleration acting over the time of the fall.
To test the hypothesis that acceleration is independent of the object's velocity, a student could conduct an experiment by launching balls at different velocities from the same height and measuring the time taken to hit the ground. This data can show that despite different initial velocities, the acceleration due to gravity remains constant for each ball, as evidenced by the same acceleration value calculated from their descent.