Question

What is the time required for an object starting at rest to fall freely 500 meters near earth surface

Answer 1

Without air resistance . . .

           Distance  =  1/2 g T²

               500 m  =  (1/2) (9.8 m/s²) (T²)

               500 m  =  (4.9 m/s²) (T²)

Divide each side by   (4.9 m/s²)  :

                  T²  =  (500 m) / (4.9 m/s²)

                       =     102.04 s²

                   T  =  √ (102.04 s²)

                       =       10.1 seconds       

Answer 2

Using kinematics, approximately 10.1 seconds