The distanced that an object falls is directly proportional

The distance,d, that an object falls is directly proportional to the square of the time, t, it has been in free fall. An object that has been in free fall for 8 seconds has fallen 1024 feet. Determine the distance the object has fallen if it has been falling for 3 seconds.

Solution

distance,d, that an object falls is directly proportional to the square of the time, t

d =k t²

An object that has been in free fall for 8 seconds has fallen 1024 feet

1024=k*8²

1024=k*64

k=1024/64

k=16

d =16t²

falling for 3 seconds.=>t =3

d =16*3²

d=16*9

d=144ft

distance the object has fallen =144ft