Derivation of Fourth Equation of Motion (Graphical Method)

Distance travelled in n^th second
= Distance travelled in n second - Distance travelled in (n-1) second

V_n = Velocity of the object in n^th second

V_n-1=velocity of the object in (n-1)^th second

Area of B'B''D''D'

= ½(Sum of parallel sides)×(Height)

=½(B'D'+B''D'')×D'D''

= ½(v_n-1+v_n)×[n-(n-1)]

= ½[(u+a(n-1)+(u+an)]×1 [∵ v=u+at]

= ½[2u+a(n-1+n)]

= ½[2u+a(2n-1)]

S_nth=u+(a/2)(2n-1)