Please answer this question in full Suppose you are driving a car in a countercl

Question

Please answer this question in full

Suppose you are driving a car in a counterclockwise direction on a circular road whose radius is r = 350 m (see the figure). You look at the speedometer and it reads a steady 30.7 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 4.82 x 10^-2 rad/s in a time of 4.05 s. What is the tangential acceleration (magnitude and direction) of the car?

Explanation / Answer

here,

radius of the circular road , r = 350 m

tangential speed of car , v = 30.7 m/s

(a)

angular speed of car , w = v/r

w = 30.7/350

w = 0.0877 rad/s

angular speed of car is 0.0877 rad/s

(b)

accelration of the car towards the centre be a

a = v^2/r

a = 30.7^2/350

a = 2.69 m/s^2

accelration of the car towards the centre is 2.69 m/s^2

(c)

time for reducing , t = 4.05 s

w1 = 0.0482 rad/s

let the final velocity be v1

v1 = r*w1

v1 = 350 * 0.0482

v1 = 16.87 m/s^2

using first equation of motion

v = u + a * t

16.87 = 30.7 + a * 4.05

a = - 3.41 m/s^2

the tangential accelration , at = 3.41/r

at = 3.41 / 350

at = 9.76*10^-3 rad/s^2

the tangential accelration is 9.76*10^-3 rad/s^2 and direction is opposite to the car motion

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