Given data:
* The radius of the circular motion of the car is r = 48.2 m.
* The acceleration of the car is,
[tex]a=8.05ms^{-2}[/tex]Solution:
The centripetal force acting on the car in terms of the acceleration is,
[tex]F=ma[/tex]The centripetal force acting on the car in terms of velocity and radius is,
[tex]F=\frac{mv^2}{r}[/tex]As the force acting on the car is the same in either case, thus,
[tex]\begin{gathered} \frac{mv^2}{r}=ma \\ \frac{v^2}{r}=a \\ v^2=ra \\ v=\sqrt[]{ra} \end{gathered}[/tex]Substituting the known values,
[tex]\begin{gathered} v=\sqrt[]{48.2\times8.05} \\ v=19.7\text{ m/s} \end{gathered}[/tex]Thus, the velocity of the car is 19.7 meters per second.
