A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 20 m/s north, and the total acceleration of the car is 2.5 m/s2 37$\degree$ south of west. Which of the following is correct?
A)R = 0.40 km, and the car's speed is decreasing.
B)R = 0.20 km, and the car's speed is decreasing.
C)R = 0.20 km, and the car's speed is increasing.
D)R = 0.16 km, and the car's speed is increasing.
E)R = 0.16 km, and the car's speed is decreasing.

Question

Quizplus · Accepted Answer

The radial component of acceleration is responsible for circular motion and can be calculated using $ a_r = \frac{v^2}{R} $. The tangential component affects speed change. Given the angle south of west, the tangential component is negative, indicating decreasing speed. Solving for R with the radial component gives 0.20 km.

A Car Travels in a Flat Circle of Radius R °\degree°

A Car Travels in a Flat Circle of Radius R $\degree$