The position of an object moving along $X$ -axis is given as $x=a+b{t}^2$, where $a, b$ are constants and $t$ is time in seconds. The object covers a distance of $16 \mathrm{m}$ in $2 \mathrm{secs}$. If the average velocity of the object between $t=3 \sec$ and $t=5 \mathrm{s}$ is $28 \mathrm{m} {\mathrm{s}}^{-1}$, the values of $a$ and $b$ are: