A car is moving at a speed of `72 km//h`. The diameter of its wheels is `0.5 m`. If the wheels are stopped in `20` rotations by applying brakes, calcualte the angular retardation produced by the brakes.

Options

A. `-25.5 "rad"//s^(2)`
B. `-29.5 "rad"//s^(2)`
C. `-33.5 "rad"//s^(2)`
D. `-45.5 "rad"//s^(2)`

Answer

A

Explanation

`v= 72 xx (5)/(18)= 20 m//s, omega_(0) = (v)/(r)= (20)/(0.25)= 80` rad/sec
`theta= 2pi xx 20= 40pi` rad
`omega^(2)= omega_(0)^(2) + 2 alpha theta`
`rArr alpha= - ((80)^(2))/(2 xx 40 pi)= (-80)/(pi)= -25.5` rad/sec