$\text{ Given }\mathrm{S}=3\mathrm{t}+6{\mathrm{t}}^2\text{ (in SI units) then }$

$\text{ Given that equation of motion of a body is }s=3t+6t^2\text{ (in SI units) }$

$\text{ On comparing this equation with }s=ut+\frac{1}{2}{\mathrm{at}}^2$

We get u = 3 (SI units) , a = 12 (SI units)

We can claim the following are true

i) The initial velocity is 3m/s

ii) The acceleration is  12/s²

iii) We get displacement of particle in t = 2s as

$\mathrm{u}=3\mathrm{m}/\mathrm{s},a=12\mathrm{m}/{\mathrm{s}}^2,\mathrm{t}=2\mathrm{s}$

$\text{ Using equations }=ut+\frac{1}{2}{\mathrm{at}}^2$

$s=3\left(2\right)+\frac{1}{2}\times 12\times 4$

$\begin{array}{r}=6+24\\ \mathrm{s}=30\mathrm{m}\end{array}$

iv) We can get displacement of particle after t = 4s as

$\mathrm{u}=3\mathrm{m}/\mathrm{s},\mathrm{a}=12\mathrm{m}/{\mathrm{s}}^2$

$\text{ Using equations }=ut+\frac{1}{2}{\text{ at }}^2$

$s=3\left(4\right)+\frac{1}{2}\left(12\right)16$

$=12+96$

$\mathrm{s}=108\mathrm{m}$

Therefore we get options a, b, c are only true