The velocity of a particle moving on a straight line varies as v=At²+Bt/(C+t), where A, B and C are constants. The dimensions of ABC are:
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The velocity of a particle moving on a straight line varies as v=At²+Bt/(C+t), where A, B and C are constants. The dimensions of ABC are:

G1 Physics · Accepted Answer

Since [v]=LT⁻¹, from At² we get [A]=LT⁻³. In Bt/(C+t), C and t must have dimension T, and the \fraction \fraction \fraction is dimensionless in time, so [B]=LT⁻¹ and [C]=T. Thus [ABC]=(LT⁻³)(LT⁻¹)(T)=L²T⁻³.