Non-uniform Circular Motion

1) If the centripetal acceleration of a car
turning a circular corner is 1.30 m/s^{2} while slowing at a rate of
0.650 m/s^{2}, what is the magnitude of the car’s total acceleration?
Also, draw a sketch showing the car’s velocity and acceleration vectors.

2) A car accelerates from 4.5 m/s to 8.6 m/s over 2.5 s, while turning a corner with a radius of 31 m. Find the magnitude of the tangential and radial accelerations when the car’s instantaneous speed is 7.5 m/s.

3) The magnitude of a car’s total acceleration
is 4.5 m/s^{2} while turning a circular corner. At the instant the car
is heading north, its speed is 6.4 m/s and its total acceleration is 28° to the west of
north. What is the radius of the circle?