The velocity of a particle v at an instant t is given by v = at +$bt^2$ the dimension of b is

[L] $[LT^{-1}]$ $[LT^{-2}]$ $[LT^{-3}]$

$[LT^{-3}]$

According to principle of dimensional Analysis Dimension of terms on LHS and RHS must be equal. Hence dimension of $at ,bt^2$ is same as that of v. ⇒ $[bt^2]$ = $[LT^{-1}]$ ⇒ [b] = $[LT^{-3}]$