The velocity v of a particle depends on time t as : v =At² + Bt + C where v is in m/s and t in second. What is the unit of C ?

The correct option is ms⁻¹.

To find the unit of the constant $C$ in the given equation:
$v=A{t}^2+Bt+C$

We apply the Principle of Homogeneity of Dimensions. According to this principle, the terms on both sides of a physical equation must have the same dimensions. This also means that we can only add or subtract physical quantities that have the exact same dimensions and units.

Since the term $C$ is added to other terms to equal the velocity $v$, the unit of $C$ must be the same as the unit of velocity $v$.

We are given that the velocity $v$ is measured in meters per second (m/s). Expressed in index notation:
Unit of velocity $v={\text{ms}}^{\mathrm{-1}}$

Therefore, the unit of $C$ must also be ms⁻¹.