5. An object is released from rest on a planet that has no atmosphere. The object falls freely for 3.0 meters in the first second. What is the magnitude of the acceleration due to gravity on the planet? l. 5 m/s^23.0 m/s^26.0 m/s^210.0 m/s^212.0 m/s^2

the acceleration due to gravity is g = 6 m/s² (option C)

Explanation:

if we ignore air friction, the height h an object falls under a gravity g is calculated through:

h = h₀ + v₀*t - 1/2*g*t²

where

t = time to reach a height h

v₀ = initial vertical velocity of the object = 0 m/s (since is released from rest)

g = gravity

h₀ = initial height = 3m

if the object starts at height h₀ = 3 m then it finishes at height h = 0 m when it falls 3 meters.

then since v₀=0 m/s:

h = h₀ - 1/2*g*t²

replacing values

0 = 3 m - 1/2*g * (1 s) ²

g = 2 * (3m - 0m) / (1 s) ² = 6 m/s²

g = 6 m/s² (option C)