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

v^2=1500

v=38.7 m/s

**Thus, the car cannot exceed 38.7 m/s.**