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^2determine 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