Velocity $(v)$ and acceleration $(a)$ in two systems of units $1$ and $2$ are related as $V _{2}=\frac{ n }{ m ^{2}} v _{1}$ and $a_{2}=\frac{a_{1}}{m n}$ respectively. Here $m$ and $n$ are constants. The relations for distance and time in two systems respectively are

• A

  $\frac{ n ^{3}}{ m ^{3}} L _{1}= L _{2}$ and $\frac{ n ^{2}}{ m } T _{1}= T _{2}$

• B

  $L_{1}=\frac{n^{4}}{m^{2}} L_{2}$ and $T_{1}=\frac{n^{2}}{m} T_{2}$

• C

  $L _{1}=\frac{ n ^{2}}{ m } L _{2}$ and $T _{1}=\frac{ n ^{4}}{ m ^{2}} T _{2}$

• D

  $\frac{ n ^{2}}{ m } L _{1}= L _{2}$ and $\frac{ n ^{4}}{ m ^{2}} T _{1}= T _{2}$