Practice problem

Centripetal Force

The magnitude of centripetal acceleration in uniform circular motion is is $\dfrac{v^2}{R}$ , where $v$ is the speed of the object and $R$ is the radius of the circle.

A particle is traveling in a circular orbit of radius as shown in the figure. At the point marked P, its velocity is found to be decreasing with time.

If $r = 2.1$ m, $v_P = 7.5$ m/s, and the rate at which the particle is slowing down is $a_{\text{tan}} = -1.5m/s^2$ , then what is the magnitude and direction of the total acceleration of the particle (taking direction C to be north)?