Derive the expression for displacement in the nth second.
a = accelleration
v = velocity, u=initial velocity
s = distance
s = ut + 1/2at2
To calculate the distance traveled during the nth second, you calculate the distance covered in n seconds and subtract the distance covered in n-1 seconds and get
s = un-u(n-1) + 1/2an2-1/2a(n-1)2
simplifying gives us
u term = u(n-(n-1)) = u*1 = u
(n-1)2 = n2-2n+1
a term = 1/2a(n2-(n-1)2) = 1/2a(n2-n2+2n-1) the n2’s cancel and give us 1/2a(2n-1) .
Final equation for displacement in the nth second is
s = u + 1/2a(2n-1)