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# The velocity v of a particle at time t is given by $v=a+ bt+\large\frac{c}{t+d}$ where a, b, c and d are constants. The dimensions of a, b c and d are respectively

From Dimensional Analysis' Principle of Homogeneity, $[a] = [v]$
$[a] = [LT^{-1}]$ and $[bt] = [v] \rightarrow [b] = \large\frac{[v]}{[t]}$$=\large\frac{[LT^{-1}]}{[T]} \Rightarrow [b] = [LT^{-2}] Also, [d] = [t] = T \Rightarrow \large\frac{[c]}{[d+t]}$$= [v] \rightarrow [c] = [v][d+t]$
$\Rightarrow [c] = [LT^{-1}]{[T]} = [L]$