The velocity v of a particle at time t is given by the equation v = At + B t + C + D . Match the constants in List-I with their dimensional formulas in List-II. List-I List-II (A) Constant A (I) [L] (B) Constant B (II) [T] (C) Constant C (III) [L T⁻¹] (D) Constant D (IV) [L T⁻²] Choose the correct answer from the options given below:

Step-by-step solution

According to the principle of homogeneity of dimensions, only quantities with the same dimensions can be added or subtracted. In the denominator (t + C) , the constant C is added to time t . Therefore, [C] = [t] = [T] . Each term in the equation must have the same dimensions as velocity v , which is [L T⁻¹] . For the term D : [D] = [v] = [L T⁻¹] . For the term At : [A][t] = [v] [A][T] = [L T⁻¹] [A] = [L T⁻²] . For the term B t + C : [B] [T] = [L T⁻¹] [B] = [L] . Thus, the correct matching is (A)-(IV), (B)-(I), (C)-