Question

Check the correctness of the relation $S_{nth}=u+\frac{a}{2}(2n-1)$, where $u$ is initial velocity, $a$ is acceleration and $S_{nth}$is the distance travelled by the body in $nth$ second.

Answer 1

$s_{nth}=\mu +\frac{a}{2}(2n-1)$

The real formula is ;

$\mu \left(1\right)+\frac{a}{2}\left(1\right)$ (2n - 1 )

where 1 represent 1 sec as times

LHS = [ L ]

[ L ] = $\mu \left(1\right)=\left[L{T}^{-1}\right]\left[T\right]$

= [ L ]

$\frac{a}{a}\left(1\right)[2n-1]$ = $L{T}^{-2}$ [ T ] [ T ]

= L

[ L ] = [ L ] + [ L ]

hence the formula is correct