# Determine the maximum constant speed a race car

Determine the maximum constant speed a race car can have if the acceleration of the car cannot exceed 7.5 m/s^2 while rounding a track having a radius of curvature of 200 m.

#### Solution:

Since the speed of the race car is constant, it has no tangential acceleration. Thus, we only need to worry about the normal acceleration. Normal acceleration is found by:

$a_n=\dfrac{v^2}{\rho}$

(Where $a_n$ is normal acceleration, $v$ is velocity, and $\rho$ is the radius of the circle)

Knowing that the acceleration cannot exceed 7.5 m/$s^2$, let us find the velocity.

$7.5=\dfrac{v^2}{200}$

$v^2=1500$

$v=38.7$ m/s
Thus, the car cannot exceed 38.7 m/s.