Question

Derive the equation.
Derive the equation for uniform acceleration motion for the displacement covered in nth second of its motion.(sn=u+a(n-1/2)

Answer 1

istance travelled in n seconds:
S1= un + 1/2a(n^2)
distance travelled in (n-1) seconds:
S2 = u(n-1) + 1/2a((n-1)^2)
distance travelled in nth second:
S1-S2
= u + 1/2a(2n-1)

Answer 2

v = u + at

velocity at t = n-1:   u + (n-1) a
velocity at t = n  :    u + n a

average velocity during nth second :  average of above two
       =  [ 2u + a n + an - a] / 2  =  u + a (n - 1/2)
Distance traveled in nth second : in one second =  [ u + a (n -1/2) ] * 1

so the answer