How far will a free falling object have fallen from a position of rest when it's instantaneous speed is 10m/s?

Use kinematic equation:

vf² = vo² + 2g (xf - xo)

vf = final velocity = 10 m/s

vo = initial velocity = 0 m/s (i. e. at rest)

g = 9.81 m/s²

xf - xo = distance traveled = d

*rearrange equation to solve for d

(vf² - vo²) / (2g) = d

d = ((10 m/s) ² - (0 m/s) ²) / (2*9.81 m/s²)

d = (100 m²/s²) / (2*9.81 m/s²)

d = 5.097 m