# A car is traveling along a circular curve

A car is traveling along a circular curve that has a radius of 50 m. If its speed is 16 m/s and is increasing uniformly at 8 m/$s^2$determine the magnitude of its acceleration at this instant.

#### Solution:

The tangential acceleration, $a_t$ is equal to 8 m/$s^2$. We now need to find the normal acceleration since the car is travelling along a circular curve. We can use the following formula to do so:

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

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

$a_n=\dfrac{16^2}{50}=5.12$ m/$s^2$

The magnitude of acceleration is:

$a=\sqrt{(a_t)^2+(a_n)^2}$

$a=\sqrt{8^2+5.12^2}=9.5$ m/$s^2$