Final answer:
The velocity of a dropped rock does indeed increase linearly due to the constant acceleration of gravity, which makes the first statement true. However, the second statement is false because the kinetic energy decreases as the rock is thrown up and increases as it falls down, rather than the potential energy increasing with the rock's velocity on the descent.
Step-by-step explanation:
The statement 'If you drop a rock its velocity increases by 32 feet per second for each additional second it falls' suggests the velocity is a linear function of time, which is true. The acceleration due to gravity, which in this case is equivalent to 32 feet per second squared (9.80 m/s2), is a constant rate of increase in velocity. Therefore, if a rock is dropped and not thrown, its velocity increases linearly as it falls due to gravity. This is represented by the equation v = gt, where 'v' is velocity, 'g' is the acceleration due to gravity, and 't' is time.
In physics, the concept of energy is crucial for understanding the motion of objects. When a rock is thrown into the air, its kinetic energy decreases as it rises and its potential energy increases. However, when it falls back down, its potential energy decreases, converting back into kinetic energy; therefore, the increase in velocity does not increase potential energy, it increases kinetic energy. So the statement that 'the increase in height would increase the rock's kinetic energy' is false, as the increase in height increases potential energy, not kinetic energy. Additionally, 'the increase in velocity as it falls to the ground would increase its potential energy' is also false; it is kinetic energy that increases as velocity increases on the way down.