The velocity, of particle is related to time according to equation V=Ct^3. The dimensions of constant c are
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Dimension of v = LT^-1
So, dimensions of Ct^3 should also be equal to dimensions of velocity (principle of homogeneity).
So,
[Ct^3] = [LT^-1]
Or,
[C] = [(LT^-1)/(T^3)]
[C] = [LT^-2]
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