The velocity v of a particle at time t is given by  v = at+bt+cwhere a, b and c are constants. The dimensions of a, b and c are respectively.

: According to principle of homogeneity of dimensions, the dimensions of all the terms in a physical expression should be the same.The given expression is  v = at+bt+cFrom principle of homogeneityat = vSimilarly [c] = [t] ; b= [L]Or [b] = [L]Note : If a physical quantity depends on more than three factors, then relation among them cannot be established because we can have only three equations by equating the powers of M.L and T.