An object starts falling under gravity from rest. If it completes 9/25 of its journey within the last second. Find the total time taken and the total displacement?
The object must complete 16/25 of its fall prior to the last second, in time t-1. Let t be the total time taken.
(1/2)g (t-1)^2 = (16/25)(1/2) g t^2
That can be simplified to
(t-1)^2 = 16/25 t^2
(t-1)/t = 4/5
t = 5 s
Now compute the distance that it falls in that time.