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^2determine the magnitude of its acceleration at this instant.


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:


(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{8^2+5.12^2}=9.5 m/s^2


This question can be found in Engineering Mechanics: Dynamics, 13th edition, chapter 12, question 12-114.

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