A truck is moving at a speed of 54 km/h. The radius of its wheels is 50 cm. On applying the brakes the wheels stop after 20 rotations. What will be the linear distance travelled by the truck during this? Also find the angular acceleration of the wheels.

Explanation

`v_(2)=0`, for stop
Here, `v_(1)=54km//h=15ms^(-1)`,
`r=50cm=0.5m`,
`theta=20` rotations = `40pi` rad,
`d=?, alpha=?`
`omega_(1)=(v_(1))/(r)=(15)/(0.5)=30" rad/s"`
`omega_(2)=(v_(2))/(r)=(0)/(0.5)=0" rad/s "(because" It stops, so "v_(2)=0)`
`alpha=(omega_(2)^(2)-omega_(1)^(2))/(2theta)=(0-(30)^(2))/(2xx40pi)`
`therefore alpha=-(900)/(80pi)=-3.5828" rad s"^(-2)`
`therefore alpha=-3.58" rad s"^(-2)`
now, 1 rotation = `2pir` linear distance
`therefore 20` rotations `=20xx2pir` distance
Linear distance travelled by the truck
`therefore d=40xx3.14xx0.5`
`therefore d=62.8m`