A race car starts from rest on a circular track of radius 400m. The car's...

Centripetal acceleration ${\displaystyle a_c}$ the following is stated
${\displaystyle a_c=R{\omega }^2=\frac{v^2}{R}}$
where ${\displaystyle v}$ is linear velocity of the object, ${\displaystyle \omega }$ is its angular velocity and ${\displaystyle R}$ is the radius of the circle in which object moves.
Tangential acceleration ${\displaystyle a_t}$ is given to be ${\displaystyle =0.500 m{s}^{-2}}$
Comparing the size of two and putting in a value ${\displaystyle R}$ we obtain
${\displaystyle \frac{v^2}{400}=0.500}$
${\displaystyle \Rightarrow v=\sqrt{0.500\times 400}=\sqrt{200}=14.142 m{s}^{-1}}$