The distance travelled by a particle starting from rest and moving with an acceleration $\frac{4}{3}{\text{ms}}^{-2}$in the third second is   

Distance travelled by the particle in nth second,

${\text{S}}_{\text{nth}}=\text{u}+\frac{1}{2}\text{a}\left(2\text{n}-1\right)$

Where u is initial speed and a is acceleration of the particle

Here, n = 3, u = 0, $\text{a}=\frac{4}{3}{\text{m/s}}^{\text{2}}$

$\therefore {\text{S}}_{\text{3rd}}=0+\frac{1}{2}\times \frac{4}{3}\times \left(2\times 3-1\right)=\frac{10}{3}\text{m}$