Question

Suppose you are driving a car in a counterclockwise direction on a circular road whose radius is r = 380 m (see the figure). You look at the speedometer and it reads a steady 31.2 m/s. (a) What is the angular speed of the car? (b) Determine the acceleration (magnitude and direction) of the car. (c) To avoid a rear-end collision with the vehicle ahead, you apply the brakes and reduce your angular speed to 5.0 × 10-2 rad/s in a time of 3.98 s. What is the tangential acceleration (magnitude and direction) of the car?

Answer 1

a)

$$\omega=\frac{v}{r}=\frac{31.2}{380}=0.0821\frac{rad}{s}$$

b)

$$a=\frac{v^2}{r}=\frac{31.2^2}{380}=2.56\frac{m}{s^2}$$

Direction: to the center of circle.

c)

$$\alpha=\frac{\omega}{t}=\frac{0.0821-0.05}{3.98}=0.00807\frac{rad}{s^2}$$

Direction: clockwise direction on a circular road.