The proof that the displacement of a body in nth second which is given by the S=u+a/2(2n-1) is explained below.
Given:
Displacement during nth second= displacement in n seconds- displacement in (n-1) seconds
= [[tex]un + \frac{1}{2} gn^2] - [ u(n-1) + \frac{1}{2} g(n-1)^2][/tex]
= (u * 1) + g(n *1) - [tex]\frac{g}{2}[/tex](1 *1)
Hence, in (n-1) seconds, n has a unit of time and 1 has a unit of time (not a constant)
Therefore, u(m/s) is multiplied by 1 (unit of time)
g(m/s^2) is multiplied by ( n*1 ), having units of time, i.e s^2
g/2 is also multiplied by ( 1 * 1, also having units of time, i.e s^2
Therefore, the equation is dimensionally correct and we should note that 1 is not a constant in the equation as the time of 1 second in (n-1) second.
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