Question

derive the equation for uniform accelerated motion for the displacement covered in its Nth second.(s_n=u+a(n-1\2)

Answer 1

Distance travelled in the nth second (Sn)=distance travelled in n (s1)seconds - distance travelled in n-1 second(s2)
sn=s1-s2
distance travelled in t seconds s=ut+1/2at²
distance travelled in n seconds s1=un+1/2 an²
Distance travelled in n-1 seconds s2=u(n-1) +1/2a(n-1)²
sn=s1-s2
=(un+1/2an²)-[u[n-1]+1/2a(n-1)²]
=un+1/2an²-[un- u+1/2a(n2-2n+1)
=un+1/2an²-un+u-1/2an²+an-1/22
=u+an-1/2a
sn=u+a[n-1/2]