A particle moving with a constant acceleration describes in the last second of it's motion 9/25th of the whole distance.of it starts from rest ,how long is the particle is in motion and through what distance does it move if it describes 6cm in first second?

Answer 1

In its first t-1 seconds, the particle moves 16/25 of the distance covered in t seconds.

(a/2)(t-1)^2 = (16/25)(a/2)t^2
(t-1)^2/t^2 = 16/25
(t-1)/t = 3/4
t = 4 seconds

(a/2)*1^2 = 0.06 m
a = 0.12 m/s^2

In 4 seconds, it moves
(a/2)*4^2 = 0.06*16 = 0.96 m