a particle starts from rest with uniform acceleration a.its velocity after n seconds is v.the displacement of the body in last two seconds is:
the distance travelled by the particle in the last two seconds will be
= distance travelled by particle in nth second - distance travelled by particle in (n-2)th second
so,
s = (1/2)an2 - (1/2)a.(n-2)2
= (1/2)a.[n2 - n2 +4n - 4]
= (a/2).[4n - 4]
so,
s = (2n-2).a = 2a.(n-1) ............................(1)
now,
velocity, v = acceleration x time
v = a x n
or
a = v/n ..........................(2)
so, the displacement in the last two seconds will be
s = 2(v/n).(n-1)