Question

Chek the correctness of the relation, `S_(n_(th)) = u +(a)/(2)(2n -1),` where u is initial velocity, a is acceleratin and `S_(n_(th))` is the distance travelled by the body in nth second.

Answer 1

The given relation is
`S_(nth) = u +(a)/(2)(2n-1)`
Writing the dimensions on either side, we get
`L.H.S = S_(nth) = ("disntance")/("time") = (L)/(T) = LT^(-1)`
`=[M^0L^1T^(-1)]`
`R.H.S. = u + (a)/(2)(2n-1) = LT^(-1) +LT^(-2)(T)`
`= LT^(-1) + LT^(-1) = LT^(-1)`
`=[M^0L^1T^(-1)].`
As LHS = RHS, dimensionally
Formula is correct.