Final answer:
The correct equation for the velocity of an object in free fall when air resistance can be ignored is B) gt. This reflects the linear relationship between velocity and time due to the constant acceleration caused by gravity.
Step-by-step explanation:
When we can ignore air resistance, the velocity v of an object that is dropped initially from rest is directly proportional to the time t it has been falling and is described by the equation v = gt, where g is the acceleration due to gravity. For an object in free fall near the Earth's surface, g is approximately 9.80 meters per second squared (m/s²). Therefore, the correct answer to the question 'When the air resistance can be ignored, the velocity of an object dropped initially from rest is given by which equation?' is B) gt. This is because the velocity of the object increases linearly with time, as gravity is a constant force acting on the object.