With the usual notations the following equation `S_(t)=u+1/2a(2t-1)` is

Options

A. Only numerically correct
B. Only dimensionally correct
C. Both numerically and dimensionally correct
D. Neither numerically nor dimensionally correct

Answer

C

Explanation

(i) Distance travelled in `t^(th)` second
`= ("Distance")/("Time") = [LT^(-1)]`
`[u] = [LT^(-1) ] , [1/2 a(2t-1)]=[LT^(-2)T]`
`=[LT^(-1)]`
Dimensionally correct.
(ii) Distance in t sec
`S_t = ut +1/2 at^2`
Distance in (t - 1)sec
`S_(t-1)=u(t-1)+1/2a(t-1)^2`
Distance travel, in `t^(th)` sec
`S_t = S-S_(t-1) =mu +1/2 a(2t-1)`
Numerically correct.