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)