If you know that the rock fell 4.9 m in 1 s, how far did it drop in the first 0.5 s after you dropped it?

When an object is free-falling, no other force is acting upon it but the gravitational force. Because of this, the equations of motion are simplified. We can determine first the initial velocity:

v = √2gy = √2 (9.81) (4.9) = 9.805 m/s

Then, we use this to the equation below:

y = vt + 1/2*at²

y = (9.805) (0.5) + 1/2 (9.81) (0.5) ²

y = 6.13 m