- #1

kalupahana

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## Homework Statement

When a car is decelerating it's speed reduces from 80 km/h to 55 km/h. In this time the wheels of car complete 55 rotations. The diameter of the wheel is 1m.

Find the

1) angular acceleration of the car.

2) time taken to stop the car if it continued in same deceleration.

## Homework Equations

v = rω

ω

^{2}

_{1}= ω

^{2}

_{0}+ 2αθ

ω

_{1}= ω

_{0}+ αt

Any equation regarding motion can be used to do this.

I used above three

## The Attempt at a Solution

55 km/h = 15.2 m/s

80 km/h = 22.2 m/s

v = rω

I got ω = v/r from it. So

ω

_{0}= 22.2 m/s

ω

_{1}= 15.2 m/s

Then I used this equation to find angular acceleration

ω

^{2}

_{1}= ω

^{2}

_{0}+ 2αθ

15.2

^{2}= 22.2

^{2}+ 2 x 55 x π x α

-261.8 = 2 x 22/7 x 55 x α

α = -0.75 rad/s

^{2}

ω

_{1}= ω

_{0}+ αt

can be use to find the time taken to stop

0 = 15.2 - 0.75t

t = 15.2/0.75 = 20.26 s

But in the textbook the answers are given as -1.5 rad/s

^{2}for angular acceleration and 20 sec for time taken to stop. But I got other things.

Please help me to complete this.

Thnx