The velocity v of a particle at time t is given by $v=at+\frac{b}{t+c}$where 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 $v=at+\frac{b}{t+c}$

From principle of homogeneity

$$\begin{gathered} \left[a\right]\left[t\right]=\left[v\right] \\ \left[a\right]=\frac{\left[\text{v}\right]}{\left[\text{t}\right]}=\frac{\left[{\text{LT}}^{-1}\right]}{\left[\text{T}\right]}=\left[{\text{LT}}^{-2}\right] \\ \left[c\right]=\left[t\right]=\left[T\right] \\ \frac{\left[b\right]}{\left[t+c\right]}=\left[v\right] \\ \left[\text{b}\right]=\left[\text{v}\right]\left[\text{t}+\text{c}\right]\text{\hspace{0.17em}\hspace{0.17em}or\hspace{0.17em}\hspace{0.17em}}\left[{\text{LT}}^{-1}\right]\left[\text{T}\right]=\left[\text{L}\right] \end{gathered}$$

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 equalizing the powers of

            M, L and T.