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The displacement of a particle is represented by $y= A t+ B t^{2}+ C t^{3}$, then what are the dimensions of A, B and C.

$\left[ LT ^{-1}\right]\left[ LT ^{-2}\right],\left[ LT ^{-3}\right]$.

L. H. S.; $y=[ L ]$, and

R. H. S.;

$A t =[ L ] ; \therefore A = L / T =\left[ LT ^{-1}\right]$

$B t^{2} =[ L ] ; \therefore B = L / T ^{2}=\left[ LT ^{-2}\right]$

$\text { and } C t^{3} =[ L ] ; \therefore C = L / T ^{3}=\left[ LT ^{-3}\right]$

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