A proton $($mass $m=1\mathrm{.}67{10}^{-27}kg)$ is being accelerated along a straight line at $3\mathrm{.}3{10}^{15}\frac{m}{s^2}$ in a particle accelerator. The proton has an initial velocity of $2\mathrm{.}4{10}^7\frac{m}{s}$ and travels $3\mathrm{.}5$ cm $.$

$($a$)$ What is its final velocity? $($Give your answer to at least four significant figures.$)$

$\frac{m}{s}$

$($b$)$ What is the increase in its kinetic energy?