Question

derive sn=u+a(n-1/2)

Answer 1

From the equations of motion of kinematics,Distance travelled in t seconds: 

S=ut+12at2

Distance travelled in n seconds:S1=un+12an2

Distance travelled in n-1 seconds:S2=un-1+12a(n-1)2

Distance travelled in nth second:Sn=S1-S2=un+12an2-un-1+12a(n-1)2

=u+12an2-n-12=u+12a(2n-1)/2

=u+a(n-1/2)